From 5c25081eb2e6f424b88b9ca523a5697ec7369c41 Mon Sep 17 00:00:00 2001 From: Riccardo Finotello Date: Tue, 20 Oct 2020 19:29:13 +0200 Subject: [PATCH] Update images and references Signed-off-by: Riccardo Finotello --- sciencestuff.sty | 8 +- sec/abstract.tex | 2 +- sec/app/ml.tex | 34 +- sec/outline.tex | 4 +- sec/part1/dbranes.tex | 10 +- sec/part1/fermions.tex | 4 +- sec/part1/introduction.tex | 230 +++--- sec/part2/divergences.tex | 4 +- sec/part2/introduction.tex | 2 +- sec/part3/conclusion.tex | 2 +- sec/part3/introduction.tex | 24 +- sec/part3/ml.tex | 6 +- thesis.bib | 1373 +++++++----------------------------- thesis.cls | 9 +- thesis.pdf | Bin 3097433 -> 3101650 bytes thesis.tex | 1 + tikz/complex_plane.pgf | 2 +- 17 files changed, 414 insertions(+), 1301 deletions(-) diff --git a/sciencestuff.sty b/sciencestuff.sty index 10b4539..b5538d7 100644 --- a/sciencestuff.sty +++ b/sciencestuff.sty @@ -50,10 +50,10 @@ \providecommand{\sm}{\textsc{sm}\xspace} \providecommand{\eom}{\textsc{e.o.m.}\xspace} -\providecommand{\cft}{\textsc{CFT}\xspace} -\providecommand{\qft}{\textsc{QFT}\xspace} -\providecommand{\qed}{\textsc{QED}\xspace} -\providecommand{\qcd}{\textsc{QCD}\xspace} +\providecommand{\cft}{\textsc{cft}\xspace} +\providecommand{\qft}{\textsc{qft}\xspace} +\providecommand{\qed}{\textsc{qed}\xspace} +\providecommand{\qcd}{\textsc{qcd}\xspace} \providecommand{\ope}{\textsc{o.p.e.}\xspace} \providecommand{\ode}{\textsc{o.d.e.}\xspace} \providecommand{\dof}{\textsc{d.o.f.}\xspace} diff --git a/sec/abstract.tex b/sec/abstract.tex index 1fcef23..aa9e681 100644 --- a/sec/abstract.tex +++ b/sec/abstract.tex @@ -12,7 +12,7 @@ We finally present a new artificial intelligence approach to algebraic geometry We compute the Hodge numbers of Complete Intersection Calabi--Yau $3$-folds using deep learning techniques based on computer vision and object recognition techniques. We also include a methodological study of machine learning applied to data in string theory: as in most applications machine learning almost never relies on the blind application of algorithms to the data but it requires a careful exploratory analysis and feature engineering. We thus show how such an approach can help in improving results by processing the data before using it. -We then show how deep learning can reach the highest accuracy in the task with smaller networks with less parameters. +We then show that the deep learning approach can reach the highest accuracy in the task with smaller networks and less parameters. This is a novel approach to the task: differently from previous attempts we focus on using convolutional neural networks capable of reaching higher accuracy on the predictions and ensuring phenomenological relevance to results. In fact parameter sharing and concurrent scans of the configuration matrix retain better generalisation properties and adapt better to the task than fully connected networks. diff --git a/sec/app/ml.tex b/sec/app/ml.tex index d1fa9bc..98a0547 100644 --- a/sec/app/ml.tex +++ b/sec/app/ml.tex @@ -11,7 +11,7 @@ A linear model learns a function \end{equation} where $w$ and $b$ are the \emph{weights} and \emph{intercept} of the fit. -One of the key assumptions behind a linear fit is the independence of the residual error between the predicted point and the value of the model, which can therefore be assumed to be sampled from a normal distribution peaked at the average value~\cite{Lista:2017:StatisticalMethodsData, Caffo::DataScienceSpecialization}. +One of the key assumptions behind a linear fit is the independence of the residual error between the predicted point and the value of the model, which can therefore be assumed to be sampled from a normal distribution peaked at the average value~\cite{Skiena:2017:DataScienceDesign, Caffo::DataScienceSpecialization}. The parameters of the fit are then chosen to maximise their \emph{likelihood} function, or conversely to minimise its logarithm with a reversed sign (the $\chi^2$ function). A related task is to minimise the mean squared error without assuming a statistical distribution of the residual error: \ml for regression usually implements this as loss function of the estimators. In this sense loss functions for regression are more general than a likelihood approach but they are nonetheless related. @@ -147,9 +147,9 @@ They are called \textit{support vectors} (accessible using the attribute \texttt As a consequence any sum involving $\alpha^{(i)}$ or $\beta^{(i)}$ can be restricted to the subset of support vectors. Using the kernel notation, the predictions will therefore be \begin{equation} - y_{pred}^{(i)} + y_{\text{pred}}^{(i)} = - y_{pred}\qty(x^{(i)}) + y_{\text{pred}}\qty(x^{(i)}) = \finitesum{n}{1}{F'} w_n \phi_n\qty(x^{(i)}) + b = @@ -215,7 +215,7 @@ In regression tasks it is usually given by the $l_1$ and $l_2$ norms of the devi \begin{equation} H^{[l]}_n\qty(x;\, t_{j,\, n}) = - \frac{1}{\abs{\cM^{[l]}_n( t_{j,\, n} )}} \sum\limits_{i \in A^{[l]}_n} \abs{y^{(i)} - \tilde{y}^{[l]}_{pred,\, n}( x )}, + \frac{1}{\abs{\cM^{[l]}_n( t_{j,\, n} )}} \sum\limits_{i \in A^{[l]}_n} \abs{y^{(i)} - \tilde{y}^{[l]}_{\text{pred},\, n}( x )}, \quad \qty( x^{(i)},\, y^{(i)} ) \in \cM_n\qty( t_{j,\, n} ), \end{equation} @@ -224,20 +224,20 @@ In regression tasks it is usually given by the $l_1$ and $l_2$ norms of the devi \begin{equation} H^{[l]}_n\qty(x;\, t_{j,\, n}) = - \frac{1}{\abs{\cM^{[l]}_n( t_{j,\, n} )}} \sum\limits_{i \in A^{[l]}_n} \qty( y^{(i)} - \bar{y}^{[l]}_{pred,\, n}( x ) )^2, + \frac{1}{\abs{\cM^{[l]}_n( t_{j,\, n} )}} \sum\limits_{i \in A^{[l]}_n} \qty( y^{(i)} - \bar{y}^{[l]}_{\text{pred},\, n}( x ) )^2, \quad \qty( x^{(i)}, y^{(i)} ) \in \cM_n( t_{j,\, n} ), \end{equation} \end{itemize} where $\abs{\cM^{[l]}_n\qty( t_{j,\, n} )}$ is the cardinality of the set $\cM^{[l]}_n\qty( t_{j,\, n} )$ for $l = 1, 2$ and \begin{equation} - \tilde{y}^{[l]}_{pred,\, n}( x ) + \tilde{y}^{[l]}_{\text{pred},\, n}( x ) = - \underset{i \in A^{[l]}_n}{\mathrm{median}}~ y_{pred}\qty(x^{(i)}), + \underset{i \in A^{[l]}_n}{\mathrm{median}}~ y_{\text{pred}}\qty(x^{(i)}), \qquad - \bar{y}^{[l]}_{pred,\, n}( x ) + \bar{y}^{[l]}_{\text{pred},\, n}( x ) = - \frac{1}{\abs{A^{[l]}_n}} \sum\limits_{i \in A^{[l]}_n} y_{pred}\qty(x^{(i)}), + \frac{1}{\abs{A^{[l]}_n}} \sum\limits_{i \in A^{[l]}_n} y_{\text{pred}}\qty(x^{(i)}), \end{equation} where $A_n^{[l]} \subset A_n$ are the subset of labels in the left and right splits ($l = 1$ and $l = 2$, that is) of the node $n$. @@ -280,7 +280,7 @@ Also random forests of trees provide a variable ranking system by averaging the As a reference, \textit{random forests} of decision trees (as in \texttt{ensemble.RandomForestRegressor} in \texttt{scikit-learn}) are ensemble learning algorithms based on fully grown (deep) decision trees. They were created to overcome the issues related to overfitting and variability of the input data and are based on random sampling of the training data~\cite{Ho:1995:RandomDecisionForests}. -The idea is to take $K$ random partitions of the training data and train a different decision tree for each of them and combine the results: for a classification task this would resort to averaging the \textit{a posteriori} (or conditional) probability of predicting the class $c$ given an input $x$ (i.e.\ the Bayesan probability $P\qty(c \mid x)$) over the $K$ trees, while for regression this amount to averaging the predictions of the trees $y_{pred,\, \hatn}^{(i)\, \lbrace k \rbrace}$ where $k = 1, 2, \dots, K$ and $\hatn$ is the final node (i.e. the node containing the final predictions). +The idea is to take $K$ random partitions of the training data and train a different decision tree for each of them and combine the results: for a classification task this would resort to averaging the \textit{a posteriori} (or conditional) probability of predicting the class $c$ given an input $x$ (i.e.\ the Bayesan probability $P\qty(c \mid x)$) over the $K$ trees, while for regression this amount to averaging the predictions of the trees $y_{\text{pred},\, \hatn}^{(i)\, \lbrace k \rbrace}$ where $k = 1, 2, \dots, K$ and $\hatn$ is the final node (i.e. the node containing the final predictions). This defines what has been called a \textit{random forest} of trees which can usually help in improving the predictions by reducing the variance due to trees adapting too much to training sets. \textit{Boosting} methods are another implementation of ensemble learning algorithms in which more \textit{weak learners}, in this case shallow decision trees, are trained over the training dataset~\cite{Friedman:2001:GreedyFunctionApproximation, Friedman:2002:StochasticGradientBoosting}. @@ -343,11 +343,13 @@ In \fc networks the input of layer $l$ is a feature vector $a^{(i)\, \qty{l}} \i } In other words, each entry of the vectors $a^{(i)\, \qty{l}}_j$ (for $j = 1, 2, \dots, n_l$) is mapped through a function $\psi$ to all the components of the following layer $a^{\qty{l+1}} \in \R^{n_{l+1}}$: \begin{equation} - \begin{split} - \psi\colon & \R^{n_l} \quad \longrightarrow \quad \R^{n_{l+1}} - \\ - & a^{(i)\, \qty{l}} \quad \longmapsto \quad a^{(i)\, \qty{l+1}} = \psi_j( a^{(i)\, \qty{l}} ), - \end{split} + \centering + \begin{tabular}{@{}rlll@{}} + $\psi\colon$ & $\R^{n_l}$ & $\longrightarrow$ & $\R^{n_{l+1}}$ + \\ + & $a^{\qty(i)\, \qty{l}}$ & $\longmapsto$ & $a^{\qty(i)\, \qty{l+1}} = \psi_j\qty( a^{\qty(i)\, \qty{l}} )$, + \\ + \end{tabular} \end{equation} such that \begin{equation} @@ -367,7 +369,7 @@ A common choice is the \textit{rectified linear unit} ($\mathrm{ReLU}$) function \end{equation} which has been proven to be better at training deep learning architectures~\cite{Glorot:2011:DeepSparseRectifier}, or its modified version $\mathrm{LeakyReLU}( z ) = \max( \alpha z, z )$ which introduces a slope $\alpha > 0$ to improve the computational performance near the non differentiable point in the origin. -\cnn architectures were born in the context of computer vision and object localisation~\cite{Tompson:2015:EfficientObjectLocalization}. +\cnn architectures rose to fame in the context of computer vision and object localisation~\cite{Tompson:2015:EfficientObjectLocalization}. As one can suspect looking at~\Cref{fig:nn:lenet} for instance, the fundamental difference with \fc networks is that they use a convolution operation $K^{\qty{l}} * a^{(i)\, \qty{l}}$ instead of a linear map to transform the output of the layers, before applying the activation function.\footnotemark{} \footnotetext{% In general the input of each layer can be a generic tensor with an arbitrary number of axis. diff --git a/sec/outline.tex b/sec/outline.tex index 516893b..b7a6bea 100644 --- a/sec/outline.tex +++ b/sec/outline.tex @@ -6,7 +6,7 @@ They are mainly based on published work~\cite{Finotello:2019:ClassicalSolutionBo However I also include some hints to future directions to cover which might expand the work shown here. The thesis is organised in three main parts plus a fourth with appendices and notes. -\Cref{part:cft} of the manuscript is dedicated to set the stage for the entire discussion and to present mathematical tools used to compute amplitudes with phenomenological relevance in string theory. +\Cref{part:cft} of the manuscript is dedicated to set the stage for the entire discussion and to present mathematical tools used to compute amplitudes with (semi-)phenomenological relevance in string theory. Namely it starts with an introduction on conformal symmetry (clearly focusing only on aspects relevant to the discussion as many reviews on the subject have already been written) and the role of compactification and D-branes in replicating results obtained in particle physics. Then the analysis of a specific setup involving angled D6-branes intersecting in non factorised internal space is presented.\footnotemark{} \footnotetext{% @@ -28,7 +28,7 @@ Namely it is hidden in contact terms and interaction with massive string states \Cref{part:deeplearning} is dedicated to state-of-the-art application of deep learning techniques to the field of string theory compactifications. The Hodge numbers of Complete Intersection Calabi--Yau $3$-folds are computed through a rigorous data science and machine learning analysis. In fact the blind application of neural networks to the configuration matrix of the manifolds can be improved by exploratory data analysis and feature engineering, from which to infer behaviour and relations of topological quantities invisibly hidden in the configuration matrix. -Deep learning techniques are then applied to the manifolds to obtain the Hodge numbers as a regression task.\footnotemark{} +Deep learning techniques are then applied to the configuration matrix of the manifolds to obtain the Hodge numbers as a regression task.\footnotemark{} \footnotetext{% Many previous approaches have proposed classification tasks to get the best performance out of machine learning models. This however implies specific knowledge of the definition interval of the Hodge numbers and does not generalise well to unknown examples of Complete Intersection Calabi--Yau manifolds. diff --git a/sec/part1/dbranes.tex b/sec/part1/dbranes.tex index 8996b42..ff4f342 100644 --- a/sec/part1/dbranes.tex +++ b/sec/part1/dbranes.tex @@ -9,13 +9,13 @@ The fermion--boson couplings and the study of flavour changing neutral currents~ Furthermore these and many other computations require the ability to calculate correlation functions of (excited) twist and (excited) spin fields. The goal of the section is therefore to address such challenges in specific scenarios. -The computation of the correlation functions of Abelian twist fields can be found in literature and plays a role in many scenarios such as magnetic branes with commuting magnetic fluxes~\cite{Angelantonj:2000:TypeIStringsMagnetised,Bertolini:2006:BraneWorldEffective,Bianchi:2005:OpenStoryMagnetic,Pesando:2010:OpenClosedString,Forste:2018:YukawaCouplingsMagnetized}, strings in gravitational wave background~\cite{Kiritsis:1994:StringPropagationGravitational,DAppollonio:2003:StringInteractionsGravitational,Berkooz:2004:ClosedStringsMisner,DAppollonio:2005:DbranesBCFTHppwave}, bound states of D-branes~\cite{Gava:1997:BoundStatesBranes,Duo:2007:NewTwistField,David:2000:TachyonCondensationD0} and tachyon condensation in Superstring Field Theory~\cite{David:2000:TachyonCondensationD0,David:2001:TachyonCondensationUsing,David:2002:ClosedStringTachyon,Hashimoto:2003:RecombinationIntersectingDbranes}. -A similar analysis can be extended to excited twist fields even though they are more subtle to treat and hide more delicate aspects~\cite{Burwick:1991:GeneralYukawaCouplings,Stieberger:1992:YukawaCouplingsBosonic,Erler:1993:HigherTwistedSector,Anastasopoulos:2011:ClosedstringTwistfieldCorrelators,Anastasopoulos:2012:LightStringyStates,Anastasopoulos:2013:ThreeFourpointCorrelators}. -Results were however found starting from dual models~\cite{Sciuto:1969:GeneralVertexFunction,DellaSelva:1970:SimpleExpressionSciuto} up to modern interpretations of string theory. +The computation of the correlation functions of Abelian twist fields can be found in literature and plays a role in many scenarios such as magnetic branes with commuting magnetic fluxes~\cite{Angelantonj:2000:TypeIStringsMagnetised,Bianchi:2005:OpenStoryMagnetic,Pesando:2010:OpenClosedString,Forste:2018:YukawaCouplingsMagnetized}, strings in gravitational wave background~\cite{Kiritsis:1994:StringPropagationGravitational,DAppollonio:2003:StringInteractionsGravitational}, bound states of D-branes~\cite{Gava:1997:BoundStatesBranes,Duo:2007:NewTwistField} and tachyon condensation in Superstring Field Theory~\cite{David:2000:TachyonCondensationD0,David:2001:TachyonCondensationUsing,Hashimoto:2003:RecombinationIntersectingDbranes}. +A similar analysis can be extended to excited twist fields even though they are more subtle to treat and hide more delicate aspects~\cite{Burwick:1991:GeneralYukawaCouplings,Stieberger:1992:YukawaCouplingsBosonic,Anastasopoulos:2012:LightStringyStates,Anastasopoulos:2013:ThreeFourpointCorrelators}. +Results were however found starting from dual models~\cite{Sciuto:1969:GeneralVertexFunction} up to modern interpretations of string theory. Correlation functions involving arbitrary numbers of plain and excited twist fields were more recently studied~\cite{Pesando:2014:CorrelatorsArbitraryUntwisted,Pesando:2012:GreenFunctionsTwist,Pesando:2011:GeneratingFunctionAmplitudes} blending the CFT techniques with the path integral approach and the canonical quantization~\cite{Pesando:2008:MultibranesBoundaryStates,DiVecchia:2007:WrappedMagnetizedBranes,Pesando:2011:StringsArbitraryConstant,DiVecchia:2011:OpenStringsSystem,Pesando:2013:LightConeQuantization}. We consider D6-branes intersecting at angles in the case of non Abelian relative rotations presenting non Abelian twist fields at the intersections. -We try to understand subtleties and technical issues arising from a scenario which has been studied only in the formulation of non Abelian orbifolds \cite{Inoue:1987:NonAbelianOrbifolds,Inoue:1990:StringInteractionsNonAbelian,Gato:1990:VertexOperatorsNonabelian,Frampton:2001:ClassificationConformalityModels} and for relative \SU{2} rotations of the D-branes ~\cite{Pesando:2016:FullyStringyComputation}. +We try to understand subtleties and technical issues arising from a scenario which has been studied only in the formulation of non Abelian orbifolds~\cite{Inoue:1987:NonAbelianOrbifolds,Inoue:1990:StringInteractionsNonAbelian,Gato:1990:VertexOperatorsNonAbelian} and for relative \SU{2} rotations of the D-branes~\cite{Pesando:2016:FullyStringyComputation}. In this configuration we study three D6-branes in $10$-dimensional Minkowski space $\ccM^{1,9}$ with an internal space of the form $\R^4 \times \R^2$ before the compactification. The D-branes are embedded as lines in $\R^2$ and as two-dimensional surfaces inside $\R^4$. We focus on the relative rotations which characterise each D-brane in $\R^4$ with respect to the others. @@ -1128,7 +1128,7 @@ Using the \rP symbol the solutions can be symbolically written as The normalisation parameters $K$ cannot however be guessed from the \rP symbol. As we are interested in finding the truly independent solutions to the original problem, we can use properties of the hypergeometric functions to reduce the number of possible choices of the integer factors in the definition of the parameters. -It is possible to show that any hypergeometric function $\hyp{a + \ffa}{b + \ffb}{c + \ffc}{z}$ can be written as a combination of \hyp{a}{b}{c}{z} and any of its contiguous functions~\cite{::NISTDigitalLibrary}. +It is possible to show that any hypergeometric function $\hyp{a + \ffa}{b + \ffb}{c + \ffc}{z}$ can be written as a combination of \hyp{a}{b}{c}{z} and any of its contiguous functions~\cite{Olver:2020:NISTDigitalLibrary}. For instance we can choose: \begin{equation} \hyp{a + \ffa}{b + \ffb}{c + \ffc}{z} diff --git a/sec/part1/fermions.tex b/sec/part1/fermions.tex index e59c9a8..708b30d 100644 --- a/sec/part1/fermions.tex +++ b/sec/part1/fermions.tex @@ -4,9 +4,9 @@ As previously pointed out, the computation of quantities such as Yukawa coupling After the analysis of the main contribution to amplitudes involving twist fields at the intersection of D-branes, we focus on the computation of correlators of (excited) spin fields. This has been a research subject for many years until the formulation found in the seminal paper by Friedan, Martinec and Shenker~\cite{Friedan:1986:ConformalInvarianceSupersymmetry} based on bosonization. In general the available techniques allow to compute only correlators involving Abelian configurations, that is configurations which can be factorized in sub-configurations having \U{1} symmetry. -Non Abelian cases have also been considered~\cite{Inoue:1987:NonAbelianOrbifolds,Inoue:1990:StringInteractionsNonAbelian,Gato:1990:VertexOperatorsNonabelian,Frampton:2001:ClassificationConformalityModels,Pesando:2016:FullyStringyComputation}, though their mathematical formulation is by far more complicated. +Non Abelian cases have also been considered~\cite{Inoue:1987:NonAbelianOrbifolds,Inoue:1990:StringInteractionsNonAbelian,Gato:1990:VertexOperatorsNonAbelian,Pesando:2016:FullyStringyComputation}, though their mathematical formulation is by far more complicated. -Despite the existence of an efficient method based on bosonization~\cite{Friedan:1986:ConformalInvarianceSupersymmetry} and old methods based on the Reggeon vertex~\cite{Sciuto:1969:GeneralVertexFunction,DellaSelva:1970:SimpleExpressionSciuto,Schwarz:1973:EvaluationDualFermion,DiVecchia:1990:VertexIncludingEmission,Nilsson:1990:GeneralNSRString,DiBartolomeo:1990:GeneralPropertiesVertices,Engberg:1993:AlgorithmComputingFourRamond,Petersen:1989:CovariantSuperreggeonCalculus}, we take into examination the computation of spin field correlators and propose a new method to compute them. +Despite the existence of an efficient method based on bosonization~\cite{Friedan:1986:ConformalInvarianceSupersymmetry} and old methods based on the Reggeon vertex~\cite{Sciuto:1969:GeneralVertexFunction,DiVecchia:1990:VertexIncludingEmission,Nilsson:1990:GeneralNSRString,DiBartolomeo:1990:GeneralPropertiesVertices,Petersen:1989:CovariantSuperreggeonCalculus}, we take into examination the computation of spin field correlators and propose a new method to compute them. We hope to be able to extend this approach to correlators involving twist fields and non Abelian spin and twist fields. We would also like to investigate the reason of the non existence of an approach equivalent to bosonization for twist fields. At the same time we are interested to explore what happens to a \cft in presence of defects. diff --git a/sec/part1/introduction.tex b/sec/part1/introduction.tex index c1e912b..9aa5b2e 100644 --- a/sec/part1/introduction.tex +++ b/sec/part1/introduction.tex @@ -28,7 +28,7 @@ Such surface can have different topologies according to the nature of the object As the action of a point particle is proportional to the length of its trajectory (its \emph{worldline}), the same object for a string is proportional to the area of the worldsheet in the original formulation by Nambu and Goto. The solutions of the classical equations of motion (\eom) are therefore strings spanning a worldsheet of extremal area. -While Nambu and Goto's formulation is fairly direct in its definition, it si usually best to work with Polyakov's action~\cite{Polyakov:1981:QuantumGeometryBosonic}: +While Nambu and Goto's formulation is fairly direct in its definition, it is usually best to work with Polyakov's action~\cite{Polyakov:1981:QuantumGeometryBosonic}: \begin{equation} S_P\qty[ \gamma, X ] = @@ -58,8 +58,8 @@ The \eom for the string $X^{\mu}\qty(\tau, \sigma)$ is therefore: \qquad \alpha,\, \beta = 0, 1. \end{equation} -In this formulation $\gamma_{\alpha\beta}$ is the worldsheet metric with Lorentzian signature $\qty(-,\, +)$. -As there are no derivatives of $\gamma_{\alpha\beta}$, its \eom is a constraint ensuring the equivalence of Polyakov's and Nambu and Goto's formulations. +In this formulation $\gamma_{\alpha\beta}$ are the components of the worldsheet metric with Lorentzian signature $\qty(-,\, +)$. +As there are no derivatives of $\gamma_{\alpha\beta}$, the \eom of the metric is a constraint ensuring the equivalence of Polyakov's and Nambu and Goto's formulations. In fact \begin{equation} \fdv{S_P\qty[\gamma,\, X]}{\gamma^{\alpha\beta}} @@ -89,7 +89,7 @@ implies = S_{NG}[X], \end{equation} -where $S_{NG}[X]$ is the Nambu--Goto action for the classical string, $\dotX = \ipd{\tau} X$ and $\pX = \ipd{\sigma} X$. +where $S_{NG}[X]$ is the Nambu--Goto action of the classical string, $\dotX = \ipd{\tau} X$ and $\pX = \ipd{\sigma} X$. The symmetries of $S_P\qty[\gamma,\, X]$ are keys to the success of the string theory framework~\cite{Polchinski:1998:StringTheoryIntroduction}. Specifically~\eqref{eq:conf:polyakov} displays symmetries under: @@ -146,7 +146,7 @@ Notice that the last is not a symmetry of the Nambu--Goto action and it only app The definition of the 2-dimensional stress-energy tensor is a direct consequence of~\eqref{eq:conf:worldsheetmetric}~\cite{Green:1988:SuperstringTheoryIntroduction}. In fact the classical constraint on the tensor is simply \begin{equation} - T_{\alpha\beta} + \cT_{\alpha\beta} = \frac{4 \pi}{\sqrt{- \det \gamma}} \fdv{S_P\qty[\gamma,\, X]}{\gamma^{\alpha\beta}} @@ -163,54 +163,54 @@ In fact the classical constraint on the tensor is simply 0. \label{eq:conf:stringT} \end{equation} -While its conservation $\nabla^{\alpha} T_{\alpha\beta} = 0$ is somewhat trivial, Weyl invariance also ensures the tracelessness of the tensor +While its conservation $\nabla^{\alpha} T_{\alpha\beta} = 0$ is somewhat trivial, Weyl invariance also ensures the vanishing trace of the tensor \begin{equation} - \trace{T} = \tensor{T}{^{\alpha}_{\alpha}} = 0. + \trace{\cT} = \tensor{\cT}{^{\alpha}_{\alpha}} = 0. \end{equation} -In other words, the $(1 + 1)$-dimensional theory of massless scalars $X^{\mu}$ in~\eqref{eq:conf:polyakov} is \emph{conformally invariant} (for review and details see \cite{Friedan:1986:ConformalInvarianceSupersymmetry,DiFrancesco:1997:ConformalFieldTheory,Ginsparg:1988:AppliedConformalField,Blumenhagen:2009:IntroductionConformalField}). +In other words, the $(1 + 1)$-dimensional theory of massless scalars $X^{\mu}$ in~\eqref{eq:conf:polyakov} is \emph{conformally invariant} (for review and details see \cite{Friedan:1986:ConformalInvarianceSupersymmetry,DiFrancesco:1997:ConformalFieldTheory,Blumenhagen:2009:IntroductionConformalField}). -Using the invariances of the actions we can set $\gamma_{\alpha\beta}(\tau, \sigma) = e^{\phi(\tau, \sigma)}\, \eta_{\alpha\beta}$, known as \emph{conformal gauge} where $\eta_{\alpha\beta} = \mathrm{diag}(-1, 1)$. -This gauge choice is however preserved by the residual \emph{pseudoconformal} transformations +Using the invariances of the actions we set $\gamma_{\alpha\beta}(\tau, \sigma) = e^{\phi(\tau, \sigma)}\, \eta_{\alpha\beta}$, known as \emph{conformal gauge} where $\eta_{\alpha\beta} = \mathrm{diag}(-1, 1)$. +This gauge choice is however preserved by the residual \emph{pseudo-conformal} transformations \begin{equation} \tau \pm \sigma = \sigma_{\pm} \quad \mapsto \quad f_{\pm}\qty(\sigma_{\pm}), \label{eq:conf:residualgauge} \end{equation} -where $f_{\pm}$ is an arbitrary function of its argument. +where $f_{\pm}$ is an arbitrary function of its argument (the subscript $\pm$ distinguishes the combination of the variables $\tau$ and $\sigma$ in it). It is natural to introduce a Wick rotation $\tau_E = i \tau$ and the complex coordinates $\xi = \tau_E + i \sigma$ and $\bxi = \xi^*$. The transformation maps the Lorentzian worldsheet to a new surface: an infinite Euclidean strip for open strings or a cylinder for closed strings. -In these terms, the tracelessness of the stress-energy tensor translates to +In these terms, the vanishing trace of the stress-energy tensor translates to \begin{equation} - T_{\xi \bxi} = 0, + \cT_{\xi \bxi} = 0, \end{equation} -while its conservation $\partial^{\alpha} T_{\alpha\beta} = 0$ becomes:\footnotemark{} +while its conservation $\partial^{\alpha} \cT_{\alpha\beta} = 0$ becomes:\footnotemark{} \footnotetext{% Since we fix $\gamma_{\alpha\beta}\qty(\tau, \sigma) \propto \eta_{\alpha\beta}$ we do not need to account for the components of the connection and we can replace the covariant derivative $\nabla^{\alpha}$ with a standard derivative $\partial^{\alpha}$. } \begin{equation} - \bpd T_{\xi\xi}\qty( \xi,\, \bxi ) + \ipd{\bxi} \cT_{\xi\xi}\qty( \xi,\, \bxi ) = - \pd \barT_{\bxi\bxi}\qty( \xi,\, \bxi ) + \ipd{\xi} \overline{\cT}_{\bxi\bxi}\qty( \xi,\, \bxi ) = 0. \end{equation} The last equation finally implies \begin{equation} - T_{\xi\xi}\qty( \xi,\, \bxi ) + \cT_{\xi\xi}\qty( \xi,\, \bxi ) = - T_{\xi\xi}\qty( \xi ) + \cT_{\xi\xi}\qty( \xi ) = - T\qty( \xi ), + \cT\qty( \xi ), \qquad - \barT_{\bxi\bxi}\qty( \xi,\, \bxi ) + \overline{\cT}_{\bxi\bxi}\qty( \xi,\, \bxi ) = - \barT_{\bxi\bxi}\qty( \bxi ) + \overline{\cT}_{\bxi\bxi}\qty( \bxi ) = - \barT\qty( \bxi ), + \overline{\cT}\qty( \bxi ), \end{equation} -which are respectively the holomorphic and the anti-holomorphic components of the bidimensional stress energy tensor. +which are respectively the holomorphic and the anti-holomorphic components of the stress energy tensor. -The previous properties define what is known as a bidimensional \emph{conformal field theory} (\cft). +The previous properties define what is known as a two-dimensional \emph{conformal field theory} (\cft). Ordinary tensor fields \begin{equation} \phi_{\omega, \bomega}\qty( \xi, \bxi ) @@ -254,17 +254,17 @@ An additional conformal transformation \end{equation} maps the worldsheet of the string to the complex plane. On this Riemann surface the usual time ordering becomes a \emph{radial ordering} as constant time surfaces are circles around the origin (see the contours $\ccC_{(0)}$ and $\ccC_{(1)}$ in \Cref{fig:conf:complex_plane}). -In these coordinates the conserved charge associated to the transformation $z \mapsto z + \epsilon(z)$ in radial quantization is +In these coordinates the conserved charge associated to the transformation $z \mapsto z + \epsilon(z)$ in radial quantization is: \begin{equation} Q_{\epsilon, \bepsilon} = \cint{0} \ddz - \epsilon(z)\, T(z) + \epsilon(z)\, \cT(z) + \cint{0} \ddbz - \bepsilon(\barz)\, \barT(\barz), + \bepsilon(\barz)\, \overline{\cT}(\barz), \end{equation} where $\ccC_0$ is an anti-clockwise constant radial time path around the origin. The transformation on a field $\phi_{\omega, \bomega}$ of weight $(\omega, \bomega)$ is thus given by the commutator with $Q_{\epsilon, \bepsilon}$: @@ -275,17 +275,17 @@ The transformation on a field $\phi_{\omega, \bomega}$ of weight $(\omega, \bome \liebraket{Q_{\epsilon, \bepsilon}}{\phi_{\omega, \bomega}\qty( w, \barw )} \\ & = - \cint{0} \ddz \epsilon(z) \qty[ T(z), \phi_{\omega, \bomega}\qty( w, \barw ) ] + \cint{0} \ddz \epsilon(z) \qty[ \cT(z), \phi_{\omega, \bomega}\qty( w, \barw ) ] + - \cint{0} \ddbz \bepsilon(\barz) \qty[ \barT(\barz), \phi_{\omega, \bomega}\qty( w, \barw ) ] + \cint{0} \ddbz \bepsilon(\barz) \qty[ \overline{\cT}(\barz), \phi_{\omega, \bomega}\qty( w, \barw ) ] \\ & = - \cint{w} \ddz \epsilon(z)\, \rR\qty( T(z)\, \phi_{\omega, \bomega}( w, \barw ) ) + \cint{w} \ddz \epsilon(z)\, \rR\qty( \cT(z)\, \phi_{\omega, \bomega}( w, \barw ) ) + - \cint{\barw} \ddbz \bepsilon(\barz)\, \rR\qty( \barT(\barz)\, \phi_{\omega, \bomega}( w, \barw ) ), + \cint{\barw} \ddbz \bepsilon(\barz)\, \rR\qty( \overline{\cT}(\barz)\, \phi_{\omega, \bomega}( w, \barw ) ), \end{split} \end{equation} -where in the last passage we used the fact that the difference of ordered integrals becomes the contour integral of the radially ordered product computed surrounding $w$. +where in the last passage we used the fact that the difference of ordered integrals becomes the contour integral of the radially ordered product computed as a infinitesimally small anti-clockwise loop around $w$. Equating the result with the expected variation \begin{equation} \begin{split} @@ -304,7 +304,7 @@ Equating the result with the expected variation we find the short distance singularities of the components of the stress-energy tensor with the field $\phi_{\omega, \bomega}( w, \barw )$: \begin{equation} \begin{split} - T( z )\, \phi_{\omega, \bomega}\qty( w, \barw ) + \cT( z )\, \phi_{\omega, \bomega}\qty( w, \barw ) & = \frac{\omega}{(z - w)^2}\, \phi_{\omega, \bomega}\qty( w, \barw ) + @@ -312,7 +312,7 @@ we find the short distance singularities of the components of the stress-energy + \order{1}, \\ - \barT( \barz )\, \phi_{\omega, \bomega}\qty( w, \barw ) + \overline{\cT}( \barz )\, \phi_{\omega, \bomega}\qty( w, \barw ) & = \frac{\bomega}{(\barz - \barw)^2}\, \phi_{\omega, \bomega}\qty( w, \barw ) + @@ -345,26 +345,26 @@ which is an asymptotic expansion containing the full information on the singular \frac{\delta_{ij}}{(z - w)^{\omega_i + \omega_j} (\barz - \barw)^{\bomega_i + \bomega_j}}. \end{equation*} } -The constant coefficients $\cC_{ijk}$ are subject to restrictive constraints given by the properties of the conformal theories to the point that a \cft is completely specified by the spectrum of the weights $(\omega_i, \bomega_i)$ and the coefficients $\cC_{ijk}$ \cite{Friedan:1986:ConformalInvarianceSupersymmetry, Ginsparg:1988:AppliedConformalField}. +The constant coefficients $\cC_{ijk}$ are subject to restrictive constraints given by the properties of the conformal theories to the point that a \cft is completely specified by the spectrum of the weights $(\omega_i, \bomega_i)$ and the coefficients $\cC_{ijk}$ \cite{Friedan:1986:ConformalInvarianceSupersymmetry}. The \ope can also be computed on the stress-energy tensor itself: \begin{equation} \begin{split} - T( z )\, T( w ) + \cT( z )\, \cT( w ) & = \frac{\frac{c}{2}}{(z - w)^4} + - \frac{2}{(z - w)^2}\, T(w) + \frac{2}{(z - w)^2}\, \cT(w) + - \frac{1}{z - w}\, \ipd{w} T(w), + \frac{1}{z - w}\, \ipd{w} \cT(w), \\ - \barT( \barz )\, \barT( \barw ) + \overline{\cT}( \barz )\, \overline{\cT}( \barw ) & = \frac{\frac{\barc}{2}}{(\barz - \barw)^4} + - \frac{2}{(\barz - \barw)^2}\, \barT(\barw) + \frac{2}{(\barz - \barw)^2}\, \overline{\cT}(\barw) + - \frac{1}{\barz - \barw}\, \ipd{\barw} \barT(\barw). + \frac{1}{\barz - \barw}\, \ipd{\barw} \overline{\cT}(\barw). \end{split} \label{eq:conf:TTexpansion} \end{equation} @@ -372,13 +372,13 @@ The components of the stress-energy tensor are therefore not primary fields and This is a reflection of the anomalous algebra of the operator modes $L_n$ and $\barL_n$ computed from the Laurent expansion \begin{equation} \begin{split} - T( z ) = \infinfsum{n} L_n\, z^{-n -2} + \cT( z ) = \infinfsum{n} L_n\, z^{-n -2} & \Rightarrow - L_n = \cint{0} \ddz z^{n + 1} T(z), + L_n = \cint{0} \ddz z^{n + 1} \cT(z), \\ - \barT( \barz ) = \infinfsum{n} \barL_n\, \barz^{-n -2} + \overline{\cT}( \barz ) = \infinfsum{n} \barL_n\, \barz^{-n -2} & \Rightarrow - \barL_n = \cint{0} \ddbz \barz^{n + 1} \barT(\barz). + \barL_n = \cint{0} \ddbz \barz^{n + 1} \overline{\cT}(\barz). \end{split} \label{eq:conf:Texpansion} \end{equation} @@ -402,7 +402,7 @@ This ultimately leads to the quantum algebra known as Virasoro algebra, unique central extension of the classical de Witt algebra, with central charge $c$. Operators $L_n$ and $\barL_n$ are called Virasoro operators.\footnotemark{} \footnotetext{% - Notice that the subset of Virasoro operators $\qty{ L_{-1},\, L_0,\, L_1 }$ forms a closed subalgebra generating the group $\SL{2}{\R}$. + Notice that the subset of Virasoro operators $\qty{ L_{-1},\, L_0,\, L_1 }$ forms a closed sub-algebra generating the group $\SL{2}{\R}$. } Notice that $L_0 + \barL_0$ is the generator of the dilations on the complex plane. In terms of radial quantization this maps to time translations and $L_0 + \barL_0$ can be considered to be the Hamiltonian of the theory. @@ -425,7 +425,7 @@ From the previous relations we can finally define the ``asymptotic'' in-states a \phi_{\omega, \bomega} \regvacuum. \end{equation} -The regularity of \eqref{eq:conf:expansion} requires +Regularity of \eqref{eq:conf:expansion} requires \begin{equation} \phi_{\omega, \bomega}^{(n, m)} \regvacuum @@ -492,9 +492,9 @@ In particular the solutions to the \eom factorise into a holomorphic and an anti and the components of the stress-energy tensor~\eqref{eq:conf:stringT} are \begin{equation} \begin{split} - T( z ) & = \ipd{z} X( z ) \cdot \ipd{z} X( z ), + \cT( z ) & = \ipd{z} X( z ) \cdot \ipd{z} X( z ), \\ - \barT( \barz ) & = \ipd{\barz} \barX( \barz ) \cdot \ipd{\barz} \barX( \barz ). + \overline{\cT}( \barz ) & = \ipd{\barz} \barX( \barz ) \cdot \ipd{\barz} \barX( \barz ). \end{split} \label{eq:conf:bosonicstringT} \end{equation} @@ -502,7 +502,7 @@ Using the normalisation of the 2-points function $\left\langle X^{\mu}( z, \barz It can be shown that in order to cancel the central charge in bosonic string theory we need to introduce a pair of conformal ghosts $b(z)$ and $c(z)$ with conformal weights $(2, 0)$ and $(-1, 0)$ respectively, together with their anti-holomorphic counterparts $\barb(z)$ and $\barc(z)$. The non vanishing components of their stress-energy tensor can be computed as:\footnotemark{} \footnotetext{% - In general a system of ghosts $b( z )$ and $c( z )$ with weight $(\lambda,\, 0)$ and $(1 - \lambda,\, 0)$ can be introduced as a standalone \cft with action~\cite{Friedan:1986:ConformalInvarianceSupersymmetry, Polchinski:1998:StringTheorySuperstring} + In general a system of ghosts $b( z )$ and $c( z )$ with weight $(\lambda,\, 0)$ and $(1 - \lambda,\, 0)$ can be introduced as a standalone \cft with action~\cite{Friedan:1986:ConformalInvarianceSupersymmetry} \begin{equation*} S = \frac{1}{2 \pi} \iint \dd{z} \dd{\barz}\, b( z )\, \ipd{\barz} c( z ). \end{equation*} @@ -514,17 +514,17 @@ The non vanishing components of their stress-energy tensor can be computed as:\f where $\varepsilon = +1$ for anti-commuting fields and $\varepsilon = -1$ for Bose statistic. Their stress-energy tensor is \begin{equation*} - T_{\text{ghost}}( z ) = - \lambda\, b( z )\, \ipd{z} c( z ) - \varepsilon\, (1 - \lambda)\, c( z )\, \ipd{z} b( z ). + \cT_{\text{ghost}}( z ) = - \lambda\, b( z )\, \ipd{z} c( z ) - \varepsilon\, (1 - \lambda)\, c( z )\, \ipd{z} b( z ). \end{equation*} Their central charge is therefore $c_{\text{ghost}} = \varepsilon\, ( 1 - 3 \cQ^2)$, where $\cQ = \varepsilon\,( 1 - 2 \lambda )$. - The ghost \cft has in general an additional \emph{ghost number} \U{1} symmetry generated by the current + The ghost \cft has an additional \emph{ghost number} \U{1} symmetry generated by the current \begin{equation*} j( z ) = - b( z )\, c( z ). \end{equation*} - In general this current is a primary field (i.e.\ it is not anomalous) when $\cQ = 0$ since + The current is a primary field (i.e.\ it is not anomalous) when $\cQ = 0$ since \begin{equation*} - T_{\text{ghost}}( z )\, j( w ) = \frac{Q}{( z - w )^3} + \order{(z - w)^{-2}}. + \cT_{\text{ghost}}( z )\, j( w ) = \frac{Q}{( z - w )^3} + \order{(z - w)^{-2}}. \end{equation*} This is the case of the worldsheet fermions in~\eqref{eq:super:action} for which $\lambda = \frac{1}{2}$. For instance the reparametrisation ghosts with $\lambda = 2$ have $Q = -3$, while the superghosts with $\lambda = \frac{3}{2}$ present $Q = 2$. @@ -532,11 +532,11 @@ The non vanishing components of their stress-energy tensor can be computed as:\f } \begin{equation} \begin{split} - T_{\text{ghost}}( z ) + \cT_{\text{ghost}}( z ) & = c( z )\, \ipd{z} b( z ) - 2\, b( z )\, \ipd{z} c( z ), \\ - \barT_{\text{ghost}}( \barz ) + \overline{\cT}_{\text{ghost}}( \barz ) & = \barc( \barz )\, \ipd{\barz} \barb( \barz ) - 2\, \barb( \barz )\, \ipd{\barz} \barc( \barz ). \end{split} @@ -551,30 +551,30 @@ From their 2-points functions we get the \ope of the components of their stress-energy tensor: \begin{equation} \begin{split} - T_{\text{ghost}}(z)\, T_{\text{ghost}}(w) + \cT_{\text{ghost}}(z)\, \cT_{\text{ghost}}(w) & = \frac{-13}{(z - w)^4} + - \frac{2}{(z - w)^2}\, T_{\text{ghost}}(z) + \frac{2}{(z - w)^2}\, \cT_{\text{ghost}}(z) + - \frac{1}{z - w}\, \ipd{z} T_{\text{ghost}}(z), + \frac{1}{z - w}\, \ipd{z} \cT_{\text{ghost}}(z), \\ - \barT_{\text{ghost}}(\barz)\, \barT_{\text{ghost}}(\barw) + \overline{\cT}_{\text{ghost}}(\barz)\, \overline{\cT}_{\text{ghost}}(\barw) & = \frac{-13}{(\barz - \barw)^4} + - \frac{2}{(\barz - \barw)^2}\, \barT_{\text{ghost}}(\barz) + \frac{2}{(\barz - \barw)^2}\, \overline{\cT}_{\text{ghost}}(\barz) + - \frac{1}{\barz - \barw}\, \ipd{\barz} \barT_{\text{ghost}}(\barz), + \frac{1}{\barz - \barw}\, \ipd{\barz} \overline{\cT}_{\text{ghost}}(\barz), \end{split} \end{equation} which show that $c_{\text{ghost}} = - 26$. The central charge is therefore cancelled in the full theory (bosonic string and reparametrisation ghosts) when the spacetime dimensions are $D = 26$. -In fact let $T_{\text{full}} = T + T_{\text{ghost}}$ and $\barT_{\text{full}} = \barT + \barT_{\text{ghost}}$, then: +In fact let $\cT_{\text{full}} = \cT + \cT_{\text{ghost}}$ and $\overline{\cT}_{\text{full}} = \overline{\cT} + \overline{\cT}_{\text{ghost}}$, then: \begin{equation} - \eval{T_{\text{full}}( z )}_{\order{(z - w)^{-4}}} + \eval{\cT_{\text{full}}( z )}_{\order{(z - w)^{-4}}} = - \eval{\barT_{\text{full}}( \barz )}_{\order{(\barz - \barw)^{-4}}} + \eval{\overline{\cT}_{\text{full}}( \barz )}_{\order{(\barz - \barw)^{-4}}} = c + c_{\text{ghost}} = @@ -586,12 +586,13 @@ In fact let $T_{\text{full}} = T + T_{\text{ghost}}$ and $\barT_{\text{full}} = \quad D = 26. \end{equation} +$\cT_{\text{full}}$ and $\overline{\cT}_{\text{full}}$ are then primary fields with conformal weight $-2$. \subsection{Superstrings} As bosonic string theory deals with commuting fields $X^{\mu}$, it is impossible to build spacetime fermions and consequently a consistent phenomenology. -It is in fact necessary to introduce worldsheet fermions (i.e.\ anti-commuting variables on the string worldsheet) as an extension to the bosonic coordinates \cite{Friedan:1986:ConformalInvarianceSupersymmetry,Polchinski:1998:StringTheorySuperstring}. +It is in fact necessary to introduce worldsheet fermions (i.e.\ anti-commuting variables on the string worldsheet) as an extension to the bosonic coordinates. We schematically and briefly recall some results due to the extension of bosonic string theory to the superstring as they will be used in what follows and mainly descend from the previous discussion. The superstring action is built as an addition to the bosonic equivalent~\eqref{eq:conf:polyakov}. @@ -611,7 +612,7 @@ In complex coordinates on the plane it is~\cite{Polchinski:1998:StringTheorySupe \eta_{\mu\nu}. \label{eq:super:action} \end{equation} -In the last expression, $\psi^{\mu}$ are $D$ two-dimensional holomorphic fermion fields with conformal weight $\qty(\frac{1}{2}, 0)$ and $\bpsi^{\mu}$ are their anti-holomorphic counterparts with weight $\qty(0, \frac{1}{2})$. Their short-distance behaviour is +In the last expression $\psi^{\mu}$ are $D$ two-dimensional holomorphic fermion fields with conformal weight $\qty(\frac{1}{2}, 0)$ and $\bpsi^{\mu}$ are their anti-holomorphic counterparts with weight $\qty(0, \frac{1}{2})$. Their short-distance behaviour is \begin{equation} \psi^{\mu}( z )\, \psi^{\nu}( w ) = \frac{\eta^{\mu\nu}}{z - w}, \qquad @@ -620,11 +621,11 @@ In the last expression, $\psi^{\mu}$ are $D$ two-dimensional holomorphic fermion In this case the components of the stress-energy tensor of the theory are: \begin{equation} \begin{split} - T( z ) + \cT( z ) & = -\frac{1}{\ap}\, \ipd{z} X( z ) \cdot \ipd{z} X( z ) - \frac{1}{2}\, \psi( z ) \cdot \ipd{z} \psi( z ), \\ - \barT( \barz ) + \overline{\cT}( \barz ) & = -\frac{1}{\ap}\, \ipd{\barz} \barX( \barz ) \cdot \ipd{\barz} \barX( \barz ) - \frac{1}{2}\, \bpsi( \barz ) \cdot \ipd{\barz} \bpsi( \barz ). \end{split} @@ -650,14 +651,14 @@ The action~\eqref{eq:super:action} is also invariant under the \emph{supersymmet - \bepsilon( \barz )\, \ipd{\barz} \barX^{\mu}( \barz ) \end{split} \end{equation} -generated by the currents $J( z ) = \epsilon( z )\, T_F( z )$ and $\barJ( \barz ) = \bepsilon( \barz )\, \barT_F( \barz )$, where $\epsilon( z )$ and $\bepsilon( \barz ) = \qty( \epsilon( z ) )^*$ are anti-commuting fermions and +generated by the currents $J( z ) = \epsilon( z )\, \cT_F( z )$ and $\barJ( \barz ) = \bepsilon( \barz )\, \overline{\cT}_F( \barz )$, where $\epsilon( z )$ and $\bepsilon( \barz ) = \qty( \epsilon( z ) )^*$ are anti-commuting fermions and \begin{equation} \begin{split} - T_F( z ) + \cT_F( z ) & = i\, \sqrt{\frac{2}{\ap}}\, \psi( z ) \cdot \ipd{z} X( z ), \\ - \barT_F( \barz ) + \overline{\cT}_F( \barz ) & = i\, \sqrt{\frac{2}{\ap}}\, \bpsi( \barz ) \cdot \ipd{\barz} \barX( \barz ) \end{split} @@ -666,23 +667,23 @@ are the \emph{supercurrents}. The central charge associated to the Virasoro algebra is in this case given by both bosonic and fermionic contributions: \begin{equation} \begin{split} - T( z )\, T( w ) + \cT( z )\, \cT( w ) & = \frac{\frac{3 D}{4}}{( z - w )^4} + - \frac{2}{( z - w )^2} T( w ) + \frac{2}{( z - w )^2} \cT( w ) + - \frac{1}{z - w} \ipd{w} T( w ) + \frac{1}{z - w} \ipd{w} \cT( w ) + \order{1}, \\ - \barT( \barz )\, \barT( \barw ) + \overline{\cT}( \barz )\, \overline{\cT}( \barw ) & = \frac{\frac{3 D}{4}}{( \barz - \barw )^4} + - \frac{2}{( \barz - \barw )^2} \barT( \barw ) + \frac{2}{( \barz - \barw )^2} \overline{\cT}( \barw ) + - \frac{1}{\barz - \barw} \ipd{\barw} \barT( \barw ) + \frac{1}{\barz - \barw} \ipd{\barw} \overline{\cT}( \barw ) + \order{1}. \end{split} @@ -692,11 +693,11 @@ The central charge is therefore $c = \frac{3}{2} D$ for the \cft defined in~\eqr As in the case of the bosonic string, in order to cancel the central charge of superstring theory we introduce the reparametrisation anti-commuting ghosts $b( z )$ and $c( z )$ and their anti-holomorphic components as well as the commuting \emph{superghosts} $\beta( z )$ and $\gamma( z )$ and their anti-holomorphic counterparts. These are conformal fields with conformal weights $\qty( \frac{3}{2},\, 0 )$ and $\qty( -\frac{1}{2},\, 0 )$. Their central charge becomes $c_{\text{ghost}} = c_{bc} + c_{\beta\gamma} = -26 + 11 = -15$ (see \cref{note:conf:ghosts} for the general computation). -When considering the full theory $T_{\text{full}} = T + T_{\text{ghost}}$ and $\barT_{\text{full}} = \barT + \barT_{\text{ghost}}$ the central charge vanishes only in 10-dimensional spacetime: +When considering the full theory $\cT_{\text{full}} = \cT + \cT_{\text{ghost}}$ and $\overline{\cT}_{\text{full}} = \overline{\cT} + \overline{\cT}_{\text{ghost}}$ the central charge vanishes only in 10-dimensional spacetime: \begin{equation} - \eval{T_{\text{full}}( z )}_{\order{(z - w)^{-4}}} + \eval{\cT_{\text{full}}( z )}_{\order{(z - w)^{-4}}} = - \eval{\barT_{\text{full}}( \barz )}_{\order{(\barz - \barw)^{-4}}} + \eval{\overline{\cT}_{\text{full}}( \barz )}_{\order{(\barz - \barw)^{-4}}} = c + c_{\text{ghost}} = @@ -721,18 +722,20 @@ In what follows we thus consider the superstring formulation in $D = 10$ dimensi It is however clear that low energy phenomena need to be explained by a $4$-dimensional theory in order to be comparable with other theoretical frameworks and experimental evidence. In this section we briefly review for completeness the necessary tools to be able to reproduce consistent models capable of describing particle physics and beyond. These results represent the background knowledge necessary to better understand more complicated scenarios involving strings. -As we will never deal directly with $4$-dimensional physics this is not a complete review and we refer to \cite{Anderson:2018:TASILecturesGeometric,Blumenhagen:2007:FourdimensionalStringCompactifications,Blumenhagen:2013:BasicConceptsString,Grana:2005:FluxCompactificationsString,Grana:2017:StringTheoryCompactifications,Krippendorf:2010:CambridgeLecturesSupersymmetry,Uranga:2005:TASILecturesString} for more in-depth explanations. +As we will never deal directly with $4$-dimensional physics this is not a complete review and we refer to \cite{Anderson:2018:TASILecturesGeometric,Blumenhagen:2007:FourdimensionalStringCompactifications,Grana:2006:FluxCompactificationsString,Grana:2017:StringTheoryCompactifications,Uranga:2005:TASILecturesString} for more in-depth explanations. In general we consider Minkowski space in $10$ dimensions $\ccM^{1,9}$. To recover $4$-dimensional spacetime we let it be defined as a product \begin{equation} - \ccM^{1,9} - = - \ccM^{1,3} \otimes \ccX_6, + \ccM^{1,9} = \ccM^{1,3} \otimes \ccX_6, \end{equation} where $\ccX_6$ is a generic $6$-dimensional manifold at this stage. -This \emph{internal} manifold $\ccX_6$ is however subject to very stringent restrictions due to mathemtical consistency conditions and physical requests. -In particular $\ccX_6$ should be a compact manifold to ``hide'' the 6 extra-dimensions computed in~\eqref{eq:super:dimensions}. +This \emph{internal} manifold $\ccX_6$ is however subject to very stringent restrictions due to mathematical consistency conditions and physical requests. +In particular $\ccX_6$ should be a \emph{compact} manifold to ``hide'' the 6 extra-dimensions computed in~\eqref{eq:super:dimensions}.\footnotemark{} +\footnotetext{% + A compact manifold \ccX is defined as a Hausdorff topological space whose open covers all have a finite subcover. + In other words \ccX is compact if for each covering atlas $\ccA = \qty{ U_{\alpha} }_{\alpha \in A}$ such that $\ccX = \bigcup\limits_{\alpha \in A} U_{\alpha}$, then $\exists \ccB = \qty{ V_{\beta} }_{\beta \in B} \subset \ccA$ finite such that $\ccX = \bigcup\limits_{\beta \in B} V_{\beta}$. +} Moreover the geometry of $\ccM^{1,3}$ should be a maximally symmetric space and there should be a $N = 1$ unbroken supersymmetry in $4$ dimensions. Finally the arising gauge group and the spectrum of fermions should be realistic (e.g.\ it should be possible to define chiral fermion states)~\cite{Candelas:1985:VacuumConfigurationsSuperstrings}. These manifolds were first conjectured to exist by Eugenio Calabi~\cite{Calabi:1957:KahlerManifoldsVanishing} and their existence was later proved by Shing-Tung Yau~\cite{Yau:1977:CalabiConjectureNew}, hence the name Calabi-Yau (\cy) manifolds. @@ -795,14 +798,6 @@ The metric is \emph{Hermitian} if g( v_p, w_p ) = g( J\, v_p, J\, w_p ) \quad \forall v_p,\, w_p \in \rT_p M - % \quad - % \Leftrightarrow - % \quad - % \tensor{g}{_{ab}} - % = - % \tensor{J}{_a^c}\, - % \tensor{J}{_b^d}\, - % \tensor{g}{_{cd}}. \end{equation} In this case we can define a $(1, 1)$-form $\omega$ as \begin{equation} @@ -811,13 +806,6 @@ In this case we can define a $(1, 1)$-form $\omega$ as g( J\, v_p, w_p ) \quad \forall v_p,\, w_p \in \rT_p M. - % \quad - % \Leftrightarrow - % \quad - % \tensor{\omega}{_{ab}} - % = - % \tensor{J}{_a^c}\, - % \tensor{g}{_{cb}}. \end{equation} $(M, J, g)$ is a \emph{Kähler} manifold if: \begin{equation} @@ -830,7 +818,7 @@ $(M, J, g)$ is a \emph{Kähler} manifold if: \label{eq:cy:kaehler} \end{equation} or equivalently $\nabla J = 0$ or $\nabla \omega = 0$, where $\nabla$ is the connection of $g$. -Notice that the operators $\pd$ and $\bpd$ are such that $\pd^2 = \bpd^2 = 0$: they replace the \emph{de Rham cohomology} operator $\mathrm{d}^2 = 0$ in complex space with the holomorphic and antiholomorphic \emph{Dolbeault cohomology} operators. +Notice that the operators $\pd$ and $\bpd$ are such that $\pd^2 = \bpd^2 = 0$: they replace the \emph{de Rham cohomology} operator $\mathrm{d}^2 = 0$ in complex space with the holomorphic and anti-holomorphic \emph{Dolbeault cohomology} operators. The covariant conservation of $J$ and $\omega$ implies that the holonomy group must preserve these objects in $\R^{2m}$. Thus we have $\mathrm{Hol}(g) \subseteq \U{m} \subset \OO{2m}$. @@ -847,7 +835,7 @@ In local complex coordinates a Hermitian metric is such that g_{\bara b}\, \dd{\barz}^{\bara} \otimes \dd{z}^b, \end{equation} thus the Kähler form becomes $\omega = i g_{a\barb}\, \dd{z}^a \wedge \dd{\barz}^{\barb}$. -The relation~\eqref{eq:cy:kaehler} then translates into: +Relation~\eqref{eq:cy:kaehler} translates into: \begin{equation} \dd{\omega} = @@ -894,7 +882,7 @@ As a consequence the Ricci tensor becomes \pdv{\tensor{\Gamma}{^{\barc}_{\bara\barc}}}{z^b}. \end{equation} -Since \cy manifolds present $\mathrm{Hol}(g) \subseteq \SU{m}$, the trace part of the coefficients of the connection vanishes. +Since for \cy manifolds $\mathrm{Hol}(g) \subseteq \SU{m}$, the trace part of the coefficients of the connection vanishes. \cy manifolds thus have $\tensor{R}{_{\bara b}} = 0$, that is they are complex Ricci-flat Kähler manifolds with \SU{m} holonomy. @@ -905,21 +893,21 @@ Since \cy manifolds present $\mathrm{Hol}(g) \subseteq \SU{m}$, the trace part o They can be characterised in different ways. For instance the study of the cohomology groups of the manifold has a direct connection with the analysis of topological invariants. -For real manifolds $\tildeM$ of dimension $2m$, closed $p$-forms $\omega$ are always defined up to an \emph{exact} term. +For real manifolds $\tildeM$ of dimension $2m$, closed $p$-forms $\tomega$ are always defined up to an \emph{exact} term. In fact: \begin{equation} - \dd{\omega'_{(p)}} = \dd{(\omega_{(p)} + \dd{\eta_{(p-1)}})} = 0 + \dd{\tomega'_{(p)}} = \dd{\qty(\tomega_{(p)} + \dd{\teta_{(p-1)}})} = 0 \label{eq:cy:closedform} \end{equation} -implies an equivalence relation $\omega'_{(p)} \sim \omega_{(p)} + \dd{\eta_{(p-1)}}$. -This translates to the fact that elements of the de Rham cohomology group $H^{(p)}_{\mathrm{d}}\qty(\tildeM, \R)$ are equivalence classes $[ \omega ]$ computed through the operator $\mathrm{d}$. +implies an equivalence relation $\tomega'_{(p)} \sim \tomega_{(p)} + \dd{\teta_{(p-1)}}$. +This translates to the fact that elements of the de Rham cohomology group $H^{(p)}_{\mathrm{d}}\qty(\tildeM, \R)$ are equivalence classes $[ \tomega ]$ computed through the operator $\mathrm{d}$. The term $b^{p} = \dim{H^{(p)}_{\mathrm{d}}( \tildeM, \R )}$ counts the total number of possible $p$-forms we can build on $\tildeM$, up to \emph{gauge transformations}. These are known as \emph{Betti numbers}. The extension to the Dolbeault cohomology in complex space is possible through the operators $\pd$ and $\bpd$ over $(r, s)$-forms on manifolds $M$ of complex dimension $m$. The equivalence relation~\eqref{eq:cy:closedform} has a similar expression in complex space as \begin{equation} - \omega'_{(r,s)} \sim \omega_{(r,s)} + \bpd \omega_{(r,s-1)}, + \omega'_{(r,s)} \sim \omega_{(r,s)} + \bpd \eta_{(r,s-1)}, \end{equation} or an equivalent formulation using $\pd$. The cohomology group in this case is $H^{(r,s)}_{\bpd}( M, \C )$ and the relation with the real counterpart is @@ -979,8 +967,8 @@ These results will also be the starting point of~\Cref{part:deeplearning} in whi \subsection{D-branes and Open Strings} Dirichlet branes, or \emph{D-branes}, are another key mathematical object in string theory. -They are naturally included as extended hypersurfaces supporting strings with open topology and as physical objects with charge and tension~\cite{Polchinski:1995:DirichletBranesRamondRamond,Polchinski:1996:TASILecturesDBranes,DiVecchia:1999:DbranesStringTheory,DiVecchia:2000:BranesStringTheory,DiVecchia:1997:ClassicalPbranesBoundary,Taylor:2003:LecturesDbranesTachyon,Taylor:2004:DBranesTachyonsString,Johnson:2000:DBranePrimer}. -They are relevant in the definition of phenomenological models in string theory as they can be arranged to support chiral fermions and bosons in \sm-like scenarios as well as beyond~\cite{Honecker:2012:FieldTheoryStandard,Lust:2009:LHCStringHunter,Zwiebach::FirstCourseString}. +They are naturally included as extended hypersurfaces supporting strings with open topology and as physical objects with charge and tension~\cite{Polchinski:1995:DirichletBranesRamondRamond,Polchinski:1996:TASILecturesDBranes,DiVecchia:1999:DbranesStringTheory,DiVecchia:2000:BranesStringTheory,DiVecchia:1997:ClassicalPbranesBoundary}. +They are relevant in the definition of phenomenological models in string theory as they can be arranged to support chiral fermions and bosons in \sm-like scenarios as well as beyond~\cite{Honecker:2012:FieldTheoryStandard,Lust:2009:LHCStringHunter}. We are ultimately interested in their study to construct Yukawa couplings in string theory. @@ -1116,7 +1104,7 @@ Imposing physical conditions~\eqref{eq:conf:physical} and the \emph{level matchi where $\rN = \finitesum{n}{1}{+\infty}\, \alpha_{-n} \cdot \alpha_n$ and $\brN = \finitesum{n}{1}{+\infty}\, \balpha_{-n} \cdot \balpha_n$. We then notice that as $R \to \infty$ all states with $m \neq 0$ become infinitely massive while the states for $m = 0$ and all values of $n$ become a continuum. Conversely, as $R \to 0$ all states with $n \neq 0$ become infinitely heavy. -In field theory this would translate into a reduction of the number of dimensions since the remaining fields would be independent of the compact coordinate~\cite{Polchinski:1996:TASILecturesDBranes,Zwiebach::FirstCourseString}. +In field theory this would translate into a reduction of the number of dimensions since the remaining fields would be independent of the compact coordinate. However in closed string theory as $R \to 0$ the compactified dimension is again present. As seen in~\eqref{eq:dbranes:closedspectrum} the mass spectra of the theories compactified at radius $R$ or $\ap\, R^{-1}$ are the same under the exchange of $n$ and $m$. @@ -1136,7 +1124,7 @@ defining the dual coordinate \subsubsection{D-branes from T-duality} -Consider the case of open strings satisfying the \eom~\eqref{eq:tduality:eom} and the coundary conditions~\eqref{eq:tduality:bc}. +Consider the case of open strings satisfying the \eom~\eqref{eq:tduality:eom} and the boundary conditions~\eqref{eq:tduality:bc}. The usual mode expansion~\eqref{eq:tduality:modes} here leads to: \begin{equation} X^{\mu}( z, \barz ) @@ -1207,14 +1195,14 @@ The procedure can be generalised to $p$ coordinates, constraining the string to This geometric interpretation of the Dirichlet branes and boundary conditions is the basis for the definition of more complex scenarios in which multiple D-branes are inserted in spacetime. D-branes are however much more than mathematical entities. -They also present physical properties such as tension and charge~\cite{DiVecchia:1997:ClassicalPbranesBoundary,DiVecchia:2006:BoundaryStateMagnetized,Polchinski:1995:DirichletBranesRamondRamond}. +They also present physical properties such as tension and charge~\cite{Polchinski:1995:DirichletBranesRamondRamond,DiVecchia:1997:ClassicalPbranesBoundary,DiVecchia:2006:BoundaryStateMagnetized}. However these aspects will not be discussed here as the following analysis will mainly focus on geometrical aspects of D-branes in spacetime. \subsubsection{Gauge Groups from D-branes} As previously stated, in order to recover $4$-dimensional physics we need to compactify the $6$ extra-dimensions of the superstring. -There are in general multiple ways to do such operation consistently~\cite{Brown:1988:NeutralizationCosmologicalConstant,Bousso:2000:QuantizationFourformFluxes,Susskind:2003:AnthropicLandscapeString,tHooft:2009:DimensionalReductionQuantum,Kachru:2003:SitterVacuaString}. +There are in general multiple ways to do such operation consistently~\cite{Bousso:2000:QuantizationFourformFluxes,Susskind:2003:AnthropicLandscapeString,Kachru:2003:SitterVacuaString}. Reproducing the \sm or beyond \sm spectra are however strong constraints on the possible compactification procedures~\cite{Cleaver:2007:SearchMinimalSupersymmetric,Lust:2009:LHCStringHunter}. Many of the physical requests usually involve the introduction of D-branes and the study of open strings in order to be able to define chiral fermions and realist gauge groups. @@ -1223,7 +1211,7 @@ Specifically a Dp-brane breaks the original \SO{1,\, D-1} symmetry to $\SO{1,\, \footnotetext{% Notice that usually $D = 10$ in the superstring formulation ($D = 26$ for purely bosonic strings), but we keep a generic indication of the spacetime dimensions when possible. } -The massless spectrum of the theory on the D-brane is easily computed in lightcone gauge~\cite{Goddard:1973:QuantumDynamicsMassless,Polchinski:1998:StringTheoryIntroduction,Green:1988:SuperstringTheoryIntroduction,Angelantonj:2002:OpenStrings}. +The massless spectrum of the theory on the D-brane is easily computed in lightcone gauge~\cite{Goddard:1973:QuantumDynamicsMassless,Angelantonj:2002:OpenStrings}. Using the residual symmetries~\eqref{eq:conf:residualgauge} of the two-dimensional diffeomorphism (i.e.\ harmonic functions of $\tau$ and $\sigma$) we can set \begin{equation} X^+\qty( \tau, \sigma ) = x_0^+ + 2 \ap\, p^+\, \tau, @@ -1316,7 +1304,7 @@ These are the basic building blocks for a consistent string phenomenology involv Being able to describe gauge bosons and fermions is not enough. Physics as we test it in experiments poses stringent constraints on what kind of string models we can use. -For instance there is no way to describe chirality by simply using parallel D-branes and strings stretching among them, while requiring the existence of fermions transforming in different representations of the gauge group is necessary to reproduce \sm results~\cite{Aldazabal:2000:DBranesSingularitiesBottomUp}. +For instance there is no way to describe chirality by simply using parallel D-branes and strings stretching among them, while requiring the existence of fermions transforming in different representations of the gauge group is necessary to reproduce \sm results~\cite{Aldazabal:2000:DBranesSingularitiesBottomUp, Ibanez:2012:StringTheoryParticle}. For instance, in the low energy limit it is possible to build a gauge theory of the strong force using a stack of $3$ coincident D-branes and an electroweak sector using $2$ D-branes. These stacks would separately lead to a $\U{3} \times \U{2}$ gauge theory. @@ -1334,7 +1322,7 @@ We therefore need to introduce more D-branes to account for all the possible com An additional issue comes from the requirement of chirality. Strings stretched across D-branes are naturally massive but, in the field theory limit, a mass term would mix different chiralities. We thus need to include a symmetry preserving mechanism for generating the mass of fermions. -In string theory there are ways to deal with the requirement~\cite{Uranga:2003:ChiralFourdimensionalString,Uranga:2005:TASILecturesString,Zwiebach::FirstCourseString,Aldazabal:2000:DBranesSingularitiesBottomUp}. +In string theory there are ways to deal with the requirement~\cite{Uranga:2003:ChiralFourdimensionalString,Aldazabal:2000:DBranesSingularitiesBottomUp,Zwiebach:2009:FirstCourseString}. These range from D-branes located at singular points of orbifolds to D-branes intersecting at angles. In this manuscript we focus on intersecting D6-branes filling the $4$-dimensional spacetime and whose additional $3$ dimensions are embedded in a \cy 3-fold (e.g.\ as lines in a factorised torus $T^6 = T^2 \times T^2 \times T^2$). This D-brane geometry supports chiral fermion states at their intersection: while some of the modes of the stretched string become indeed massive, the spectrum of the fields is proportional to combinations of the angles and some of the modes can remain massless. @@ -1350,7 +1338,7 @@ The light spectrum is thus composed of the desired matter content alongside with \label{fig:dbranes:smbranes} \end{figure} -It is therefore possible to recover a \sm-like construction using multiple D-branes at angles as in~\Cref{fig:dbranes:smbranes}, where the angles have been drawn perpendicular but can in principle be arbitrary~\cite{Ibanez:2001:GettingJustStandard,Grimm:2005:EffectiveActionType,Sheikh-Jabbari:1998:ClassificationDifferentBranes,Berkooz:1996:BranesIntersectingAngles}. +It is therefore possible to recover a \sm-like construction using multiple D-branes at angles as in~\Cref{fig:dbranes:smbranes}, where the angles have been drawn perpendicular but can in principle be arbitrary~\cite{Ibanez:2001:GettingJustStandard,Sheikh-Jabbari:1998:ClassificationDifferentBranes,Berkooz:1996:BranesIntersectingAngles}. For instance quarks are localised at the intersection of the \emph{baryonic} stack of D-branes, yielding the colour symmetry generators, with the \emph{left} and \emph{right} stacks, leading to the $\qty( \vb{3}, \vb{2} )$ and $\qty( \vb{3}, \vb{1})$ representations. The same applies to leptons created by strings attached to the \emph{leptonic} stack. Combinations of the additional \U{1} factors in the resulting gauge group finally lead to the definition of the hypercharge $Y$. @@ -1364,7 +1352,7 @@ Fermions localised at the intersection of the D-branes are however naturally $4$ The presence of compactified dimensions however leads to phenomena such as \emph{family replications} of the fermions. With accurate calibration it is in fact possible to recover the quark and lepton families in the \sm. Consider for example the simple \cy factorised manifold $T^6 = T^2 \times T^2 \times T^2$ and introduce stacks of D6-branes as lines in each of the bi-tori. -Even though the lines might never intersect on a plane, they can have points in common on a torus due to the identifications~\cite{Zwiebach::FirstCourseString}. +Even though the lines might never intersect on a plane, they can have points in common on a torus due to the identifications~\cite{Zwiebach:2009:FirstCourseString}. Since each intersections supports a different set of fermions with different spectrum, the angles of the intersecting branes can be calibrated to reproduce the separation in mass of the families of quarks and leptons in the \sm. diff --git a/sec/part2/divergences.tex b/sec/part2/divergences.tex index abf461f..6dcff17 100644 --- a/sec/part2/divergences.tex +++ b/sec/part2/divergences.tex @@ -49,14 +49,14 @@ We then go back to string theory and we verify that in the \nbo the open string We then introduce the generalised Null Boost Orbifold (\gnbo) as a generalisation of the \nbo which still has a light-like singularity and is generated by one Killing vector. However in this model there are two directions associated with $\cA$, one compact and one non compact. -We can then construct the scalar \qed and the effective field theory which extends it with the inclusion of higher order terms since all terms have a distributional interpretation~\cite{Estrada:2012:GeneralIntegral}. +We can then construct the scalar \qed and the effective field theory which extends it with the inclusion of higher order terms since all terms have a distributional interpretation. However if a second Killing vector is used to compactify the formerly non compact direction, the theory has again the same problems as in the \nbo. In the literature there are however also other attempts at regularizing the \nbo such as the Null Brane. This kind of orbifold was originally defined in \cite{Figueroa-OFarrill:2001:GeneralisedSupersymmetricFluxbranes,Cornalba:2004:TimedependentOrbifoldsString} and studied in perturbation theory in \cite{Liu:2002:StringsTimeDependentOrbifolds}. The Null Brane shares with the \gnbo the existence of a non compact direction on the orbifold. In this case it is indeed possible to build single particle wave functions which leads to the convergence of the smeared amplitudes. -We finally present also a brief examination of the Boost Orbifold (\bo) where the divergences are generally milder~\cite{Horowitz:1991:SingularStringSolutions,Khoury:2002:BigCrunchBig}. +We finally present also a brief examination of the Boost Orbifold (\bo) where the divergences are generally milder~\cite{Horowitz:1991:SingularStringSolutions}. The scalar eigenfunctions behave in time $t$ as $\abs{t}^{\pm i\, \frac{l}{\Delta}}$ near the singularity but there is one eigenfunction which behaves as $\log(\abs{t})$ and again it is the constant eigenfunction along the compact direction which is the origin of all divergences. In particular the scalar \qed on the \bo can be defined and the first term which gives a divergent contribution is of the form $\abs{\phi~\dphi}^2$, i.e.\ divergences are hidden into the derivative expansion of the effective field theory. Again three points open string amplitudes with one massive state diverge. diff --git a/sec/part2/introduction.tex b/sec/part2/introduction.tex index 76ba7f3..94fec36 100644 --- a/sec/part2/introduction.tex +++ b/sec/part2/introduction.tex @@ -56,7 +56,7 @@ The $n$-dimensional \emph{orbifold} $\ccO$ is finally defined as a paracompact H In string theory the notion of orbifold has a more stringent characterisation with respect to pure mathematics. Differently from the general definition, orbifolds in physics usually appear as a global orbit space $M / G$ where $M$ is a manifold and $G$ the group of its isometries, often leading to the presence of \emph{fixed points} (i.e.\ points in the manifold which are left invariant by the action of $G$) where singularities emerge due to the presence of additional degrees of freedom given by \emph{twisted states} of the string~\cite{Dixon:1985:StringsOrbifolds,Dixon:1986:StringsOrbifoldsII}. They are commonly introduced as singular limits of \cy manifolds~\cite{Candelas:1985:VacuumConfigurationsSuperstrings}, which in turn can be recovered using algebraic geometry to smoothen the singular points. -However they can also be used to model peculiar time-dependent backgrounds~\cite{Horowitz:1991:SingularStringSolutions,Khoury:2002:BigCrunchBig,Figueroa-OFarrill:2001:GeneralisedSupersymmetricFluxbranes,Cornalba:2002:NewCosmologicalScenario,Cornalba:2004:TimedependentOrbifoldsString,Craps:2006:BigBangModels,Bachas:2002:NullBraneIntersections,Bachas:2003:RelativisticStringPulse}. +However they can also be used to model peculiar time-dependent backgrounds~\cite{Horowitz:1991:SingularStringSolutions,Figueroa-OFarrill:2001:GeneralisedSupersymmetricFluxbranes,Cornalba:2002:NewCosmologicalScenario,Cornalba:2004:TimedependentOrbifoldsString,Craps:2006:BigBangModels,Bachas:2002:NullBraneIntersections,Bachas:2003:RelativisticStringPulse}. They are in fact good toy models to study Big Bang scenarios in string theory. We focus specifically on the study of such cosmological singularities in the framework of string theory defined on time-dependent orbifolds. diff --git a/sec/part3/conclusion.tex b/sec/part3/conclusion.tex index 281a934..85e6aa1 100644 --- a/sec/part3/conclusion.tex +++ b/sec/part3/conclusion.tex @@ -10,7 +10,7 @@ For instance we could try to set up a map from any matrix to its favourable repr This could be the basis for the use of adversarial networks~\cite{Goodfellow:2014:GenerativeAdversarialNets} capable of generating the favourable embedding from the first. Or on the contrary one could generate more matrices for the same manifold in order to increase the size of the training set. Another possibility is to use the graph representation of the configuration matrix to which is automatically invariant under permutations~\cite{Hubsch:1992:CalabiyauManifoldsBestiary} (another graph representation has been decisive in~\cite{Krippendorf:2020:DetectingSymmetriesNeural} to get a good accuracy). -Techniques such as (variational) autoencoders~\cite{Kingma:2014:AutoEncodingVariationalBayes, Rezende:2014:StochasticBackpropagationApproximate, Salimans:2015:MarkovChainMonte}, cycle GAN~\cite{Zhu:2017:UnpairedImagetoimageTranslation}, invertible neural networks~\cite{Ardizzone:2019:AnalyzingInverseProblems}, graph neural networks~\cite{Gori:2005:NewModelLearning, Scarselli:2004:GraphicalbasedLearningEnvironments} or more generally techniques from geometric deep learning~\cite{Monti:2017:GeometricDeepLearning} could be helpful. +Techniques such as (variational) autoencoders~\cite{Kingma:2014:AutoEncodingVariationalBayes, Rezende:2014:StochasticBackpropagationApproximate}, cycle GAN~\cite{Zhu:2017:UnpairedImagetoimageTranslation}, invertible neural networks~\cite{Ardizzone:2019:AnalyzingInverseProblems}, graph neural networks~\cite{Gori:2005:NewModelLearning, Scarselli:2004:GraphicalbasedLearningEnvironments} or techniques from geometric deep learning~\cite{Monti:2017:GeometricDeepLearning} could be helpful. Finally our techniques apply directly to \cicy $4$-folds~\cite{Gray:2013:AllCompleteIntersection, Gray:2014:TopologicalInvariantsFibration}. However there are many more manifolds in this case (around \num{e6}) and more Hodge numbers, such that one can expect to reach a better accuracy for the different Hodge numbers (the different learning curves for the $3$-folds indicate that the model training would benefit from more data). diff --git a/sec/part3/introduction.tex b/sec/part3/introduction.tex index 925f8c5..56fc110 100644 --- a/sec/part3/introduction.tex +++ b/sec/part3/introduction.tex @@ -2,24 +2,24 @@ In the previous parts we presented mathematical tools for the theoretical interp The ultimate goal of the analysis is to provide some insights on the predictive capabilities of the string theory framework applied to phenomenological data. As already argued in~\Cref{sec:CYmanifolds} the procedure is however quite challenging as there are different ways to match string theory with the experimental reality, that is there are several different vacuum configurations arising from the compactification of the extra-dimensions. The investigation of feasible phenomenological models in a string framework has therefore to deal also with computational aspects related to the exploration of the \emph{landscape}~\cite{Douglas:2003:StatisticsStringTheory} of possible vacua. -Unfortunately the number of possibilities is huge (numbers as high as $\num{e272000}$ have been suggested for some models)~\cite{Lerche:1987:ChiralFourdimensionalHeterotic, Douglas:2003:StatisticsStringTheory, Ashok:2004:CountingFluxVacua, Douglas:2004:BasicResultsVacuum, Douglas:2007:FluxCompactification, Taylor:2015:FtheoryGeometryMost, Schellekens:2017:BigNumbersString, Halverson:2017:AlgorithmicUniversalityFtheory, Taylor:2018:ScanningSkeleton4D, Constantin:2019:CountingStringTheory}, the mathematical objects entering the compactifications are complex and typical problems are often NP-complete, NP-hard, or even undecidable~\cite{Denef:2007:ComputationalComplexityLandscape, Halverson:2019:ComputationalComplexityVacua, Ruehle:2020:DataScienceApplications}, making an exhaustive classification impossible. +Unfortunately the number of possibilities is huge (numbers as high as $\num{e272000}$ have been suggested for some models)~\cite{Douglas:2003:StatisticsStringTheory, Ashok:2004:CountingFluxVacua, Taylor:2015:FtheoryGeometryMost, Taylor:2018:ScanningSkeleton4D, Constantin:2019:CountingStringTheory}, the mathematical objects entering the compactifications are complex and typical problems are often NP-complete, NP-hard, or even undecidable~\cite{Denef:2007:ComputationalComplexityLandscape, Halverson:2019:ComputationalComplexityVacua}, making an exhaustive classification impossible. Additionally there is no single framework to describe all the possible (flux) compactifications. As a consequence each class of models must be studied with different methods. This has in general discouraged, or at least rendered challenging, precise connections to the existing and tested theories (in particular, the \sm of particle physics). Until recently the string landscape has been studied using different methods such as analytic computations for simple examples, general statistics, random scans or algorithmic enumerations of possibilities. -This has been a large endeavor of the string community~\cite{Grana:2006:FluxCompactificationsString, Lust:2009:SeeingStringLandscape, Ibanez:2012:StringTheoryParticle, Brennan:2018:StringLandscapeSwampland, Halverson:2018:TASILecturesRemnants, Ruehle:2020:DataScienceApplications}. +This has been a large endeavor of the string community~\cite{Grana:2006:FluxCompactificationsString, Brennan:2018:StringLandscapeSwampland}. The main objective of such studies is to understand what are the generic predictions of string theory. -The first conclusion of these studies is that compactifications giving an effective theory close to the Standard Model are scarce~\cite{Dijkstra:2005:ChiralSupersymmetricStandard, Dijkstra:2005:SupersymmetricStandardModel, Blumenhagen:2005:StatisticsSupersymmetricDbrane, Gmeiner:2006:OneBillionMSSMlike, Douglas:2007:LandscapeIntersectingBrane, Anderson:2014:ComprehensiveScanHeterotic}. +The first conclusion of these studies is that compactifications giving an effective theory close to the Standard Model are scarce~\cite{Dijkstra:2005:ChiralSupersymmetricStandard, Blumenhagen:2005:StatisticsSupersymmetricDbrane, Douglas:2007:LandscapeIntersectingBrane, Anderson:2014:ComprehensiveScanHeterotic}. The approach however has limitations mainly given by lack of a general understanding or high computational power required to run the algorithms. -In reaction to these difficulties and starting with the seminal paper~\cite{Abel:2014:GeneticAlgorithmsSearch} new investigations based on Machine Learning (\ml) appeared in the recent years, focusing on different aspects of the string landscape and of the geometries used in compactifications~\cite{Krefl:2017:MachineLearningCalabiYau, Ruehle:2017:EvolvingNeuralNetworks, He:2017:MachinelearningStringLandscape, Carifio:2017:MachineLearningString, Altman:2019:EstimatingCalabiYauHypersurface, Bull:2018:MachineLearningCICY, Cole:2019:TopologicalDataAnalysis, Klaewer:2019:MachineLearningLine, Mutter:2019:DeepLearningHeterotic, Wang:2018:LearningNonHiggsableGauge, Ashmore:2019:MachineLearningCalabiYau, Brodie:2020:MachineLearningLine, Bull:2019:GettingCICYHigh, Cole:2019:SearchingLandscapeFlux, Faraggi:2020:MachineLearningClassification, Halverson:2019:BranesBrainsExploring, He:2019:DistinguishingEllipticFibrations, Bies:2020:MachineLearningAlgebraic, Bizet:2020:TestingSwamplandConjectures, Halverson:2020:StatisticalPredictionsString, Krippendorf:2020:DetectingSymmetriesNeural, Otsuka:2020:DeepLearningKmeans, Parr:2020:ContrastDataMining, Parr:2020:PredictingOrbifoldOrigin} (see also~\cite{Erbin:2018:GANsGeneratingEFT, Betzler:2020:ConnectingDualitiesMachine, Chen:2020:MachineLearningEtudes, Gan:2017:HolographyDeepLearning, Hashimoto:2018:DeepLearningAdS, Hashimoto:2018:DeepLearningHolographic, Hashimoto:2019:AdSCFTCorrespondence, Tan:2019:DeepLearningHolographic, Akutagawa:2020:DeepLearningAdS, Yan:2020:DeepLearningBlack, Comsa:2019:SupergravityMagicMachine, Krishnan:2020:MachineLearningGauged} for related works and~\cite{Ruehle:2020:DataScienceApplications} for a comprehensive summary of the state of the art). +In reaction to these difficulties and starting with the seminal paper~\cite{Abel:2014:GeneticAlgorithmsSearch} new investigations based on Machine Learning (\ml) appeared in the recent years, focusing on different aspects of the string landscape and of the geometries used in compactifications~\cite{Krefl:2017:MachineLearningCalabiYau, Ruehle:2017:EvolvingNeuralNetworks, He:2017:MachinelearningStringLandscape, Carifio:2017:MachineLearningString, Altman:2019:EstimatingCalabiYauHypersurface, Bull:2018:MachineLearningCICY, Mutter:2019:DeepLearningHeterotic, Ashmore:2020:MachineLearningCalabiYau, Brodie:2020:MachineLearningLine, Bull:2019:GettingCICYHigh, Cole:2019:SearchingLandscapeFlux, Faraggi:2020:MachineLearningClassification, Halverson:2019:BranesBrainsExploring, Bizet:2020:TestingSwamplandConjectures, Halverson:2020:StatisticalPredictionsString, Krippendorf:2020:DetectingSymmetriesNeural, Otsuka:2020:DeepLearningKmeans, Parr:2020:ContrastDataMining, Parr:2020:PredictingOrbifoldOrigin} (see~\cite{Ruehle:2020:DataScienceApplications} for a comprehensive summary of the state of the art). In fact \ml is definitely adequate when it comes to pattern search or statistical inference starting from large amount of data. This motivates two main applications to string theory: the systematic exploration of the space of possibilities (if they are not random then \ml should be able to find a pattern) and the deduction of mathematical formulas from the \ml approximation. -The last few years have seen a major uprising of \ml, and more particularly of neural networks (\nn)~\cite{Bengio:2017:DeepLearning, Chollet:2018:DeepLearningPython, Geron:2019:HandsOnMachineLearning}. +The last few years have seen a major uprising of \ml, and more particularly of neural networks (\nn)~\cite{Goodfellow:2017:DeepLearning, Chollet:2018:DeepLearningPython, Geron:2019:HandsOnMachineLearning}. This technology is efficient at discovering and predicting patterns and now pervades most fields of applied sciences and of the industry. One of the most critical places where progress can be expected is in understanding the geometries used to describe string compactifications and this will be the object of study in the following analysis. -We mainly refer to~\cite{Geron:2019:HandsOnMachineLearning, Chollet:2018:DeepLearningPython, Bengio:2017:DeepLearning} for reviews in \ml and deep learning techniques, and to~\cite{Ruehle:2020:DataScienceApplications, Skiena:2017:DataScienceDesign, Zheng:2018:FeatureEngineeringMachine} for applications of data science techniques. +We mainly refer to~\cite{Geron:2019:HandsOnMachineLearning, Chollet:2018:DeepLearningPython, Goodfellow:2017:DeepLearning} for reviews in \ml and deep learning techniques, and to~\cite{Ruehle:2020:DataScienceApplications, Skiena:2017:DataScienceDesign, Zheng:2018:FeatureEngineeringMachine} for applications of data science techniques. We address the question of computing the Hodge numbers $\hodge{1}{1} \in \N$ and $\hodge{2}{1} \in \N$ for \emph{complete intersection Calabi--Yau} (\cicy) $3$-folds~\cite{Green:1987:CalabiYauManifoldsComplete} using different \ml algorithms. A \cicy is completely specified by its \emph{configuration matrix} (whose entries are positive integers) which is the basic input of the algorithms. @@ -68,7 +68,7 @@ Code is available on \href{https://thesfinox.github.io/ml-cicy/}{Github}. As presented in~\Cref{sec:CYmanifolds}, a \cy $n$-fold is a $n$-dimensional complex manifold $X$ with \SU{n} holonomy (dimension in \R is $2n$). An equivalent definition is the vanishing of its first Chern class. -A standard reference for the physicist is~\cite{Hubsch:1992:CalabiyauManifoldsBestiary} (see also~\cite{Anderson:2018:TASILecturesGeometric, He:2020:CalabiYauSpacesString} for useful references). +A standard reference for the physicist is~\cite{Hubsch:1992:CalabiyauManifoldsBestiary} (see also~\cite{Anderson:2018:TASILecturesGeometric} for useful references). The compactification on a \cy leads to the breaking of large part of the supersymmetry which is phenomenologically more realistic than the very high energy description with intact supersymmetry. \cy manifolds are characterised by a certain number of topological properties (see~\Cref{sec:cohomology_hodge}), the most salient being the Hodge numbers \hodge{1}{1} and \hodge{2}{1}, counting respectively the Kähler and complex structure deformations, and the Euler characteristics:\footnotemark{} @@ -79,14 +79,14 @@ The compactification on a \cy leads to the breaking of large part of the supersy \chi = 2 \qty(\hodge{1}{1} - \hodge{2}{1}). \label{eq:cy:euler} \end{equation} -Interestingly topological properties of the manifold directly translate into features of the $4$-dimensional effective action (in particular the number of fields, the representations and the gauge symmetry)~\cite{Hubsch:1992:CalabiyauManifoldsBestiary, Becker:2006:StringTheoryMTheory}.\footnotemark{} +Interestingly topological properties of the manifold directly translate into features of the $4$-dimensional effective action (in particular the number of fields, the representations and the gauge symmetry)~\cite{Hubsch:1992:CalabiyauManifoldsBestiary}.\footnotemark{} \footnotetext{% Another reason for sticking to topological properties is that there is no \cy manifold for which the metric is known. Hence it is not possible to perform explicitly the Kaluza--Klein reduction in order to derive the $4$-dimensional theory. -}% +} In particular the Hodge numbers count the number of chiral multiplets (in heterotic compactifications) and the number of hyper- and vector multiplets (in type II compactifications): these are related to the number of fermion generations ($3$ in the Standard Model) and is thus an important measure of the distance to the Standard Model. -The simplest \cy manifolds are constructed by considering the complete intersection of hypersurfaces in a product $\cA$ of projective spaces $\mathds{P}^{n_i}$ (called the ambient space)~\cite{Green:1987:CalabiYauManifoldsComplete, Green:1987:PolynomialDeformationsCohomology, Candelas:1988:CompleteIntersectionCalabiYau, Green:1989:AllHodgeNumbers, Anderson:2017:FibrationsCICYThreefolds, Anderson:2018:TASILecturesGeometric}: +The simplest \cy manifolds are constructed by considering the complete intersection of hypersurfaces in a product $\cA$ of projective spaces $\mathds{P}^{n_i}$ (called the ambient space)~\cite{Green:1987:CalabiYauManifoldsComplete, Green:1987:PolynomialDeformationsCohomology, Candelas:1988:CompleteIntersectionCalabiYau, Green:1989:AllHodgeNumbers, Anderson:2017:FibrationsCICYThreefolds}: \begin{equation} \cA = \mathds{P}^{n_1} \times \cdots \times \mathds{P}^{n_m}. \end{equation} @@ -173,7 +173,7 @@ Below we show a list of the \cicy properties and of their configuration matrices \item unique Hodge number combinations: $266$ \end{itemize} - \item ``original dataset''~\cite{Candelas:1988:CompleteIntersectionCalabiYau, Green:1989:AllHodgeNumbers} + \item ``original dataset''~\cite{Candelas:1988:CompleteIntersectionCalabiYau, Green:1989:AllHodgeNumbers}: \begin{itemize} \item maximal size of the configuration matrices: $12 \times 15$ \item number of favourable matrices (excluding product spaces): $4874$ ($\num{61.8}\%$) @@ -181,7 +181,7 @@ Below we show a list of the \cicy properties and of their configuration matrices \item number of different ambient spaces: $235$ \end{itemize} - \item ``favourable dataset''~\cite{Anderson:2017:FibrationsCICYThreefolds} + \item ``favourable dataset''~\cite{Anderson:2017:FibrationsCICYThreefolds}: \begin{itemize} \item maximal size of the configuration matrices: $15 \times 18$ \item number of favourable matrices (excluding product spaces): $7820$ ($\num{99.1}\%$) diff --git a/sec/part3/ml.tex b/sec/part3/ml.tex index 249c623..5b03db4 100644 --- a/sec/part3/ml.tex +++ b/sec/part3/ml.tex @@ -302,7 +302,7 @@ Obviously the very small percentage of outliers makes the effect of removing the We compare the performances of different \ml algorithms: linear regression, support vector machines (\svm), random forests, gradient boosted trees and (deep) neural networks. We obtain the best results using deep \emph{convolutional} neural networks. In fact we present a new neural network architecture, inspired by the Inception model~\cite{Szegedy:2015:GoingDeeperConvolutions, Szegedy:2016:RethinkingInceptionArchitecture, Szegedy:2016:Inceptionv4InceptionresnetImpact} which has been developed in the field of computer vision. -We provide some details on the different algorithms in~\Cref{app:ml-algo} and refer the reader to the literature~\cite{Bengio:2017:DeepLearning, Chollet:2018:DeepLearningPython, Geron:2019:HandsOnMachineLearning, Skiena:2017:DataScienceDesign, Mehta:2019:HighbiasLowvarianceIntroduction, Carleo:2019:MachineLearningPhysical, Ruehle:2020:DataScienceApplications} for more details. +We provide some details on the different algorithms in~\Cref{app:ml-algo} and refer the reader to the literature~\cite{Goodfellow:2017:DeepLearning, Chollet:2018:DeepLearningPython, Geron:2019:HandsOnMachineLearning, Skiena:2017:DataScienceDesign, Ruehle:2020:DataScienceApplications} for more details. \subsubsection{Feature Extraction} @@ -394,7 +394,7 @@ For the same reason, the latter are not displayed for the favourable dataset. \paragraph{Visualisation of the performance} Complementary to the predictions and the accuracy results, we also provide different visualisations of the performance of the models in the form of univariate plots (histograms) and multivariate distributions (scatter plots). -In fact the usual assumption behind the statistical inference of a distribution is that the difference between the observed data and the predicted values can be modelled by a random variable called \textit{residual}~\cite{Lista:2017:StatisticalMethodsData,Caffo::DataScienceSpecialization}.\footnotemark{} +In fact the usual assumption behind the statistical inference of a distribution is that the difference between the observed data and the predicted values can be modelled by a random variable called \textit{residual}~\cite{Skiena:2017:DataScienceDesign,Caffo::DataScienceSpecialization}.\footnotemark{} \footnotetext{% The difference between the non observable \textit{true} value of the model and the observed data is known as \textit{statistical error}. The difference between residuals and errors is subtle but the two definitions have different interpretations in the context of the regression analysis: in a sense, residuals are an estimate of the errors. @@ -1232,7 +1232,7 @@ In fact this neural network is much more powerful than the previous networks we When predicting only \hodge{1}{1} it surpasses \SI{97}{\percent} accuracy using only \SI{30}{\percent} of the data for training. While it seems that the predictions suffer when using a single network for both Hodge numbers this remains much better than any other algorithm. It may seem counter-intuitive that convolutions work well on this data since they are not translation or rotation invariant but only permutation invariant. -However convolution alone is not sufficient to ensure invariances under these transformations but it must be supplemented with pooling operations~\cite{Bengio:2017:DeepLearning} which we do not use. +However convolution alone is not sufficient to ensure invariances under these transformations but it must be supplemented with pooling operations~\cite{Goodfellow:2017:DeepLearning} which we do not use. Moreover convolution layers do more than just taking translation properties into account: they allow to make highly complicated combinations of the inputs and to share weights among components to find subtler patterns than standard fully connected layers. This network is more studied in more details in~\cite{Erbin:2020:InceptionNeuralNetwork}. diff --git a/thesis.bib b/thesis.bib index 6432c4f..a7aeb00 100644 --- a/thesis.bib +++ b/thesis.bib @@ -1,10 +1,4 @@ -@article{::NISTDigitalLibrary, - title = {{{NIST}} Digital Library of Mathematical Functions}, - url = {http://dlmf.nist.gov/, Release 1.0.28 of 2020-09-15}, - key = {DLMF} -} - @article{Abadi:2015:TensorFlowLargescaleMachine, title = {{{TensorFlow}}: {{Large}}-Scale Machine Learning on Heterogeneous Systems}, author = {Abadi, Martín and Agarwal, Ashish and Barham, Paul and Brevdo, Eugene and Chen, Zhifeng and Citro, Craig and Corrado, Greg S. and Davis, Andy and Dean, Jeffrey and Devin, Matthieu and Ghemawat, Sanjay and Goodfellow, Ian and Harp, Andrew and Irving, Geoffrey and Isard, Michael and Jia, Yangqing and Jozefowicz, Rafal and Kaiser, Lukasz and Kudlur, Manjunath and Levenberg, Josh and Mané, Dandelion and Monga, Rajat and Moore, Sherry and Murray, Derek and Olah, Chris and Schuster, Mike and Shlens, Jonathon and Steiner, Benoit and Sutskever, Ilya and Talwar, Kunal and Tucker, Paul and Vanhoucke, Vincent and Vasudevan, Vijay and Viégas, Fernanda and Vinyals, Oriol and Warden, Pete and Wattenberg, Martin and Wicke, Martin and Yu, Yuan and Zheng, Xiaoqiang}, @@ -23,7 +17,7 @@ volume = {2003}, pages = {057--057}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2003/04/057}, + doi = {10/b39bd8}, abstract = {Intersecting D-brane models provide an attractive explanation of family replication in the context of string theory. We show, however, that the localization of fermion families at different brane intersections in the extra dimensions introduces flavour changing neutral currents mediated by the Kaluza-Klein excitations of the gauge fields. This is a generic feature in these models, and it implies stringent bounds on the mass of the lightest Kaluza-Klein modes (becoming severe when the compactification radii are larger than the string length). We present the full string calculation of four-fermion interactions in models with intersecting D-branes, recovering the field theory result. This reveals other stringy sources of flavour violation, which give bounds that are complementary to the KK bounds (i.e. they become severe when the compactification radii are comparable to the string length). Taken together these bounds imply that the string scale is larger than \$M\_s\textbackslash gtrsim 10\^2\$ TeV, implying that non-supersymmetric cases are phenomenologically disfavoured.}, archivePrefix = {arXiv}, eprint = {hep-ph/0303087}, @@ -41,7 +35,7 @@ volume = {2005}, pages = {072--072}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2005/06/072}, + doi = {10/bt34kd}, abstract = {We calculate Yukawa interactions at one-loop on intersecting D6 branes. We demonstrate the non-renormalization theorem in supersymmetric configurations, and show how Yukawa beta functions may be extracted. In addition to the usual logarithmic running, we find the power-law dependence on the infra-red cut-off associated with Kaluza-Klein modes. Our results may also be used to evaluate coupling renormalization in non-supersymmetric cases.}, archivePrefix = {arXiv}, eprint = {hep-th/0412206}, @@ -78,7 +72,7 @@ volume = {2014}, pages = {10}, issn = {1029-8479}, - doi = {10.1007/JHEP08(2014)010}, + doi = {10/f6v8g4}, archivePrefix = {arXiv}, eprint = {1404.7359}, eprinttype = {arxiv}, @@ -87,25 +81,6 @@ number = {8} } -@article{Akutagawa:2020:DeepLearningAdS, - title = {Deep Learning and {{AdS}}/{{QCD}}}, - author = {Akutagawa, Tetsuya and Hashimoto, Koji and Sumimoto, Takayuki}, - date = {2020}, - journaltitle = {Physical Review D}, - shortjournal = {Phys. Rev. D}, - volume = {102}, - pages = {026020}, - issn = {2470-0010, 2470-0029}, - doi = {10.1103/PhysRevD.102.026020}, - archivePrefix = {arXiv}, - eprint = {2005.02636}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/akutagawa_et_al_2020_deep_learning_and_ads-qcd4.pdf}, - keywords = {archived}, - langid = {english}, - number = {2} -} - @article{Aldazabal:2000:DBranesSingularitiesBottomUp, title = {D-{{Branes}} at {{Singularities}} : {{A Bottom}}-{{Up Approach}} to the {{String Embedding}} of the {{Standard Model}}}, shorttitle = {D-{{Branes}} at {{Singularities}}}, @@ -116,7 +91,7 @@ volume = {2000}, pages = {002--002}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2000/08/002}, + doi = {10/dxtkc6}, abstract = {We propose a bottom-up approach to the building of particle physics models from string theory. Our building blocks are Type II D-branes which we combine appropriately to reproduce desirable features of a particle theory model: 1) Chirality ; 2) Standard Model group ; 3) N=1 or N=0 supersymmetry ; 4) Three quark-lepton generations. We start such a program by studying configurations of D=10, Type IIB D3-branes located at singularities. We study in detail the case of Z\_N, N=1,0 orbifold singularities leading to the SM group or some left-right symmetricextension. In general, tadpole cancellation conditions require the presence of additional branes, e.g. D7-branes. For the N=1 supersymmetric case the unique twist leading to three quark-lepton generations is Z\_3, predicting \$\textbackslash sin\^2\textbackslash theta\_W=3/14=0.21\$. The models obtained are the simplest semirealistic string models ever built. In the non-supersymmetric case there is a three-generation model for each Z\_N, N{$>$}4, but the Weinberg angle is in general too small. One can obtain a large class of D=4 compact models by considering the above structure embedded into a Calabi Yau compactification. We explicitly construct examples of such compact models using Z\_3 toroidal orbifolds and orientifolds, and discuss their properties. In these examples, global cancellation of RR charge may be achieved by adding anti-branes stuck at the fixed points, leading to models with hidden sector gravity-induced supersymmetry breaking. More general frameworks, like F-theory compactifications, allow completely \$\textbackslash NN=1\$ supersymmetric embeddings of our local structures, as we show in an explicit example.}, archivePrefix = {arXiv}, eprint = {hep-th/0005067}, @@ -134,7 +109,7 @@ volume = {2019}, pages = {186}, issn = {1029-8479}, - doi = {10.1007/JHEP03(2019)186}, + doi = {10/gg66h4}, archivePrefix = {arXiv}, eprint = {1811.06490}, eprinttype = {arxiv}, @@ -152,25 +127,13 @@ volume = {197}, pages = {81--88}, issn = {03702693}, - doi = {10.1016/0370-2693(87)90346-7}, + doi = {10/bcmx6s}, file = {/home/riccardo/.local/share/zotero/files/amati_et_al_1987_superstring_collisions_at_planckian_energies3.pdf}, keywords = {archived}, langid = {english}, number = {1-2} } -@online{Anastasopoulos:2011:ClosedstringTwistfieldCorrelators, - title = {On Closed-String Twist-Field Correlators and Their Open-String Descendants}, - author = {Anastasopoulos, Pascal and Bianchi, Massimo and Richter, Robert}, - date = {2011}, - abstract = {In a recent paper we have proposed the possibility that the lightest massive string states could be identified with open strings living at intersections of D-branes forming small angles. In this note, we reconsider the relevant twist-field correlation functions and perform the analysis of the sub-dominant physical poles in the various channels. Our derivation is new in that it is based on the algebraic procedure for the construction of open string models starting from their closed-string `parents' rather than on the stress-tensor method. We also indicate possible generalizations and diverse applications of our approach.}, - archivePrefix = {arXiv}, - eprint = {1110.5359}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/anastasopoulos_et_al_2011_on_closed-string_twist-field_correlators_and_their_open-string_descendants5.pdf}, - keywords = {⛔ No DOI found} -} - @article{Anastasopoulos:2012:LightStringyStates, title = {Light Stringy States}, author = {Anastasopoulos, Pascal and Bianchi, Massimo and Richter, Robert}, @@ -180,7 +143,7 @@ volume = {2012}, pages = {68}, issn = {1029-8479}, - doi = {10.1007/JHEP03(2012)068}, + doi = {10/f3sx4b}, abstract = {We carefully study the spectrum of open strings localized at the intersections of D6-branes and identify the lowest massive 'twisted' states and their vertex operators, paying particular attention to the signs of the intersection angles. We argue that the masses of the lightest states scale as M\^2 \textasciitilde{} \textbackslash theta M\^2\_s and can thus be parametrically smaller than the string scale. Relying on previous analyses, we compute scattering amplitudes of massless 'twisted' open strings and study their factorization, confirming the presence of the light massive states as sub-dominant poles in one of the channels.}, archivePrefix = {arXiv}, eprint = {1110.5424}, @@ -198,7 +161,7 @@ volume = {2013}, pages = {182}, issn = {1029-8479}, - doi = {10.1007/JHEP10(2013)182}, + doi = {10/gf66b5}, abstract = {We compute three- and four-point correlation functions containing excited bosonic twist fields. Our results can be used to determine properties, such as lifetimes and production rates, of massive string excitations localised at D-brane intersections, which could be signatures of a low string scale even if the usual string resonances are inaccessible to the LHC.}, archivePrefix = {arXiv}, eprint = {1305.7166}, @@ -216,7 +179,7 @@ volume = {2008}, pages = {104--104}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2008/07/104}, + doi = {10/b6d2hk}, abstract = {In this paper, we study positive monad vector bundles on complete intersection Calabi-Yau manifolds in the context of E8 x E8 heterotic string compactifications. We show that the class of such bundles, subject to the heterotic anomaly condition, is finite and consists of about 7000 models. We explain how to compute the complete particle spectrum for these models. In particular, we prove the absence of vector-like family anti-family pairs in all cases. We also verify a set of highly non-trivial necessary conditions for the stability of the bundles. A full stability proof will appear in a companion paper. A scan over all models shows that even a few rudimentary physical constraints reduces the number of viable models drastically.}, archivePrefix = {arXiv}, eprint = {0805.2875}, @@ -234,7 +197,7 @@ volume = {2014}, pages = {47}, issn = {1029-8479}, - doi = {10.1007/JHEP01(2014)047}, + doi = {10/ghf4nq}, archivePrefix = {arXiv}, eprint = {1307.4787}, eprinttype = {arxiv}, @@ -253,7 +216,7 @@ volume = {906}, pages = {441--496}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2016.03.016}, + doi = {10/f8kd3j}, abstract = {We present a generalization of the complete intersection in products of projective space (CICY) construction of Calabi-Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility stems from the fact that they can be simply described in terms of a `configuration matrix', a matrix of integers from which many of the details of the geometries can be easily extracted. The generalization we present is to allow negative integers in the configuration matrices which were previously taken to have positive semi-definite entries. This broadening of the complete intersection construction leads to a larger class of Calabi-Yau manifolds than that considered in previous work, which nevertheless enjoys much of the same degree of calculational control. These new Calabi-Yau manifolds are complete intersections in (not necessarily Fano) ambient spaces with an effective anticanonical class. We find examples with topology distinct from any that has appeared in the literature to date. The new manifolds thus obtained have many interesting features. For example, they can have smaller Hodge numbers than ordinary CICYs and lead to many examples with elliptic and K3-fibration structures relevant to F-theory and string dualities.}, archivePrefix = {arXiv}, eprint = {1507.03235}, @@ -270,7 +233,7 @@ volume = {2017}, pages = {77}, issn = {1029-8479}, - doi = {10.1007/JHEP10(2017)077}, + doi = {10/ggkmrn}, archivePrefix = {arXiv}, eprint = {1708.07907}, eprinttype = {arxiv}, @@ -283,12 +246,12 @@ title = {{{TASI Lectures}} on {{Geometric Tools}} for {{String Compactifications}}}, author = {Anderson, Lara B. and Karkheiran, Mohsen}, date = {2018}, + doi = {10/gg66m7}, abstract = {In this work we provide a self-contained and modern introduction to some of the tools, obstacles and open questions arising in string compactifications. Techniques and current progress are illustrated in the context of smooth heterotic string compactifications to 4-dimensions. Progress is described on bounding and enumerating possible string backgrounds and their properties. We provide an overview of constructions, partial classifications, and moduli problems associated to Calabi-Yau manifolds and holomorphic bundles over them.}, archivePrefix = {arXiv}, eprint = {1804.08792}, eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/anderson_karkheiran_2018_tasi_lectures_on_geometric_tools_for_string_compactifications.pdf}, - keywords = {⛔ No DOI found} + file = {/home/riccardo/.local/share/zotero/files/anderson_karkheiran_2018_tasi_lectures_on_geometric_tools_for_string_compactifications.pdf} } @article{Angelantonj:2000:TypeIStringsMagnetised, @@ -300,7 +263,7 @@ volume = {489}, pages = {223--232}, issn = {03702693}, - doi = {10.1016/S0370-2693(00)00907-2}, + doi = {10/cc5skj}, abstract = {In the presence of internal magnetic fields, a D9 brane can acquire a D5 (or anti-D5) R-R charge, and can therefore contribute to the corresponding tadpole. In the resulting vacua, supersymmetry is generically broken and tachyonic instabilities are present. However, suitable choices for the magnetic fields, corresponding to self-dual configurations in the internal space, can yield new chiral supersymmetric vacua with gauge groups of reduced rank, where the magnetic energy saturates, partly or fully, the negative tension of the O5+ planes. These models contain Green-Schwarz couplings to untwisted R-R forms not present in conventional orientifolds.}, archivePrefix = {arXiv}, eprint = {hep-th/0007090}, @@ -313,7 +276,7 @@ title = {Open {{Strings}}}, author = {Angelantonj, Carlo and Sagnotti, Augusto}, date = {2002}, - doi = {10.1016/s0370-1573(02)00273-9}, + doi = {10/c8f2xd}, abstract = {This review is devoted to open strings, and in particular to the often surprising features of their spectra. It follows and summarizes developments that took place mainly at the University of Rome “Tor Vergata” over the last decade, and centred on world-sheet aspects of the constructions now commonly referred to as “orientifolds”. Our presentation aims to bridge the gap between the world-sheet analysis, that first exhibited many of the novel features of these systems, and their geometric description in terms of extended objects, D-branes and O-planes, contributed by many other colleagues, and most notably by J. Polchinski. We therefore proceed through a number of prototype examples, starting from the bosonic string and moving on to ten-dimensional fermionic strings and their toroidal and orbifold compactifications, in an attempt to guide the reader in a self-contained journey to the more recent developments related to the breaking of supersymmetry.}, archivePrefix = {arXiv}, eprint = {hep-th/0204089}, @@ -326,14 +289,12 @@ author = {Ardizzone, Lynton and Kruse, Jakob and Wirkert, Sebastian and Rahner, Daniel and Pellegrini, Eric W. and Klessen, Ralf S. and Maier-Hein, Lena and Rother, Carsten and Köthe, Ullrich}, date = {2019}, url = {http://arxiv.org/abs/1808.04730}, - urldate = {2020-10-10}, abstract = {In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse problem is ambiguous: one measurement may map to multiple different sets of parameters. In this setting, the posterior parameter distribution, conditioned on an input measurement, has to be determined. We argue that a particular class of neural networks is well suited for this task -- so-called Invertible Neural Networks (INNs). Although INNs are not new, they have, so far, received little attention in literature. While classical neural networks attempt to solve the ambiguous inverse problem directly, INNs are able to learn it jointly with the well-defined forward process, using additional latent output variables to capture the information otherwise lost. Given a specific measurement and sampled latent variables, the inverse pass of the INN provides a full distribution over parameter space. We verify experimentally, on artificial data and real-world problems from astrophysics and medicine, that INNs are a powerful analysis tool to find multi-modalities in parameter space, to uncover parameter correlations, and to identify unrecoverable parameters.}, archivePrefix = {arXiv}, eprint = {1808.04730}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/ardizzone_et_al_2019_analyzing_inverse_problems_with_invertible_neural_networks.pdf;/home/riccardo/.local/share/zotero/storage/NQJPI658/1808.html}, - keywords = {⛔ No DOI found}, - primaryClass = {cs, stat} + keywords = {⛔ No DOI found} } @article{Arduino:2020:OriginDivergencesTimeDependent, @@ -345,7 +306,7 @@ volume = {80}, pages = {476}, issn = {1434-6044, 1434-6052}, - doi = {10.1140/epjc/s10052-020-8010-y}, + doi = {10/gg54bw}, abstract = {We consider time-dependent orbifolds in String Theory and we show that divergences are not associated with a gravitational backreaction since they appear in the open string sector too. They are related to the non existence of the underlying effective field theory as in several cases fourth and higher order contact terms do not exist. Since contact terms may arise from the exchange of string massive states, we investigate and show that some three points amplitudes with one massive state in the open string sector are divergent on the time-dependent orbifolds. To check that divergences are associated with the existence of a discrete zero eigenvalue of the Laplacian of the subspace with vanishing volume, we construct the Generalized Null Boost Orbifold where this phenomenon can be turned on and off.}, archivePrefix = {arXiv}, eprint = {2002.11306}, @@ -355,19 +316,15 @@ } @online{Ashmore:2020:MachineLearningCalabiYau, - ids = {Ashmore:2019:MachineLearningCalabiYau}, title = {Machine Learning {{Calabi}}-{{Yau}} Metrics}, author = {Ashmore, Anthony and He, Yang-Hui and Ovrut, Burt}, date = {2020}, - url = {http://arxiv.org/abs/1910.08605}, - urldate = {2020-10-07}, + doi = {10/ghf4nr}, abstract = {We apply machine learning to the problem of finding numerical Calabi-Yau metrics. Building on Donaldson's algorithm for calculating balanced metrics on K\textbackslash "ahler manifolds, we combine conventional curve fitting and machine-learning techniques to numerically approximate Ricci-flat metrics. We show that machine learning is able to predict the Calabi-Yau metric and quantities associated with it, such as its determinant, having seen only a small sample of training data. Using this in conjunction with a straightforward curve fitting routine, we demonstrate that it is possible to find highly accurate numerical metrics much more quickly than by using Donaldson's algorithm alone, with our new machine-learning algorithm decreasing the time required by between one and two orders of magnitude.}, archivePrefix = {arXiv}, eprint = {1910.08605}, eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/ashmore_et_al_2019_machine_learning_calabi-yau_metrics.pdf;/home/riccardo/.local/share/zotero/files/ashmore_et_al_2020_machine_learning_calabi-yau_metrics.pdf;/home/riccardo/.local/share/zotero/storage/GFKCJ822/1910.html}, - keywords = {⛔ No DOI found}, - primaryClass = {hep-th, stat} + file = {/home/riccardo/.local/share/zotero/files/ashmore_et_al_2019_machine_learning_calabi-yau_metrics.pdf;/home/riccardo/.local/share/zotero/files/ashmore_et_al_2020_machine_learning_calabi-yau_metrics.pdf;/home/riccardo/.local/share/zotero/storage/GFKCJ822/1910.html} } @article{Ashok:2004:CountingFluxVacua, @@ -379,7 +336,7 @@ volume = {2004}, pages = {060--060}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2004/01/060}, + doi = {10/fqsf7n}, archivePrefix = {arXiv}, eprint = {hep-th/0307049}, eprinttype = {arxiv}, @@ -397,7 +354,7 @@ volume = {2002}, pages = {035--035}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2002/12/035}, + doi = {10/b4h4q3}, abstract = {We study pairs of planar D-branes intersecting on null hypersurfaces, and other related configurations. These are supersymmetric and have finite energy density. They provide open-string analogues of the parabolic orbifold and null-fluxbrane backgrounds for closed superstrings. We derive the spectrum of open strings, showing in particular that if the D-branes are shifted in a spectator dimension so that they do not intersect, the open strings joining them have no asymptotic states. As a result, a single non-BPS excitation can in this case catalyze a condensation of massless modes, changing significantly the underlying supersymmetric vacuum state. We argue that a similar phenomenon can modify the null cosmological singularity of the time-dependent orbifolds. This is a stringy mechanism, distinct from black-hole formation and other strong gravitational instabilities, and one that should dominate at weak string coupling. A by-product of our analysis is a new understanding of the appearance of 1/4 BPS threshold bound states, at special points in the moduli space of toroidally-compactified type-II string theory.}, archivePrefix = {arXiv}, eprint = {hep-th/0210269}, @@ -415,7 +372,7 @@ volume = {305}, pages = {286--309}, issn = {00034916}, - doi = {10.1016/S0003-4916(03)00065-4}, + doi = {10/dwshqh}, abstract = {I study a relativistic open string coupling through its endpoints to a plane wave with arbitrary temporal profile. The string's transverse oscillations respond linearly to the external field. This makes it possible to solve the classical equations, and to calculate the quantum-mechanical S-matrix in closed form. I analyze the dynamics of the string as the characteristic frequency and duration of the pulse are continuously varied. I derive, in particular, the multipole expansion in the adiabatic limit of very long wavelengths, and discuss also more violent phenomena such as shock waves, cusps and null brane intersections. Apart from their relevance to the study of time-dependence in superstring theory, these results could have other applications, such as the teleportation of gravitational wave bursts by cosmic strings.}, archivePrefix = {arXiv}, eprint = {hep-th/0212217}, @@ -431,34 +388,15 @@ journaltitle = {Journal of artificial intelligence research}, volume = {12}, pages = {149--198}, - doi = {10.1613/jair.731}, + doi = {10/gg66h8}, file = {/home/riccardo/.local/share/zotero/files/baxter_2000_a_model_of_inductive_bias_learning3.pdf} } -@book{Becker:2006:StringTheoryMTheory, - title = {String {{Theory}} and {{M}}-{{Theory}}: {{A Modern Introduction}}}, - author = {Becker, Katrin and Becker, Melanie and Schwarz, John H.}, - date = {2006}, - publisher = {{Cambridge University Press}}, - file = {/home/riccardo/.local/share/zotero/files/becker_et_al_string_theory_and_m-theory.pdf}, - isbn = {978-0-511-25486-4 978-0-521-86069-7}, - langid = {english} -} - -@book{Bengio:2017:DeepLearning, - title = {Deep Learning}, - author = {Bengio, Yoshua and Goodfellow, Ian and Courville, Aaron}, - date = {2017}, - volume = {1}, - publisher = {{MIT press Massachusetts, USA:}}, - file = {/home/riccardo/.local/share/zotero/files/bengio_et_al_2017_deep_learning.pdf} -} - @article{Bergstra:2012:RandomSearchHyperparameter, title = {Random Search for Hyper-Parameter Optimization}, author = {Bergstra, James and Bengio, Yoshua}, date = {2012}, - journaltitle = {Journal of machine learning research}, + journaltitle = {Journal of Machine Learning Research}, volume = {13}, pages = {281--305}, file = {/home/riccardo/.local/share/zotero/files/bergstra_bengio_2012_random_search_for_hyper-parameter_optimization.pdf}, @@ -475,7 +413,7 @@ volume = {480}, pages = {265--278}, issn = {05503213}, - doi = {10.1016/S0550-3213(96)00452-X}, + doi = {10/fjff5p}, abstract = {We show that configurations of multiple D-branes related by SU(N) rotations will preserve unbroken supersymmetry. This includes cases in which two D-branes are related by a rotation of arbitrarily small angle, and we discuss some of the physics of this. In particular, we discuss a way of obtaining 4D chiral fermions on the intersection of D-branes. We also rephrase the condition for unbroken supersymmety as the condition that a `generalized holonomy group' associated with the brane configuration and manifold is reduced, and relate this condition (in Type IIA string theory) to a condition in eleven dimensions.}, archivePrefix = {arXiv}, eprint = {hep-th/9606139}, @@ -492,15 +430,16 @@ volume = {2003}, pages = {031--031}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2003/03/031}, + doi = {10/c9rfmc}, abstract = {We compute string scattering amplitudes in an orbifold of Minkowski space by a boost, and show how certain divergences in the four point function are associated with graviton exchange near the singularity. These divergences reflect large tree-level backreaction of the gravitational field. Near the singularity, all excitations behave like massless fields on a 1+1 dimensional cylinder. For excitations that are chiral near the singularity, we show that divergences are avoided and that the backreaction is milder. We discuss the implications of this for some cosmological spacetimes. Finally, in order to gain some intuition about what happens when backreaction is taken into account, we study an open string rolling tachyon background as a toy model that shares some features with R\^\{1,1\}/Z.}, - annotation = {ZSCC: 0000117}, + archivePrefix = {arXiv}, + eprint = {hep-th/0212215}, + eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/berkooz_et_al_2003_comments_on_cosmological_singularities_in_string_theory.pdf}, number = {03} } @article{Berkooz:2003:StringsElectricField, - ids = {Pioline:2003:StringsElectricField}, title = {Strings in an Electric Field, and the {{Milne Universe}}}, author = {Berkooz, Micha and Pioline, Boris}, date = {2003}, @@ -509,34 +448,13 @@ volume = {2003}, pages = {007--007}, issn = {1475-7516}, - doi = {10.1088/1475-7516/2003/11/007}, + doi = {10/bh47tt}, abstract = {Arguably the simplest model of a cosmological singularity in string theory, the Lorentzian orbifold \$\textbackslash Real\^\{1,1\}/boost\$ is known to lead to severe divergences in scattering amplitudes of untwisted states, indicating a large backreaction toward the singularity. In this work we take a first step in investigating whether condensation of twisted states may remedy this problem and resolve the spacelike singularity. By using the formal analogy with charged open strings in an electric field, we argue that, contrary to earlier claims, twisted sectors do contain physical scattering states, which can be viewed as charged particles in an electric field. Correlated pairs of twisted states will therefore be produced, by the ordinary Schwinger mechanism. For open strings in an electric field, on-shell wave functions for the zero-modes are determined, and shown to analytically continue to non-normalizable modes of the usual Landau harmonic oscillator in Euclidean space. Closed strings scattering states of the Milne orbifold continue to non-normalizable modes in an unusual Euclidean orbifold of \$\textbackslash Real\^2\$ by a rotation by an irrational angle. Irrespective of the formal analogy with the Milne Universe, open strings in a constant electric field, or colliding D-branes, may also serve as a useful laboratory to study time-dependence in string theory.}, archivePrefix = {arXiv}, eprint = {hep-th/0307280}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/berkooz_pioline_2003_strings_in_an_electric_field,_and_the_milne_universe.pdf}, - issue = {11}, - number = {LPTHE-03-21, WIS-20-03-DPP} -} - -@article{Berkooz:2004:ClosedStringsMisner, - title = {Closed {{Strings}} in {{Misner Space}}: {{Stringy Fuzziness}} with a {{Twist}}}, - shorttitle = {Closed {{Strings}} in {{Misner Space}}}, - author = {Berkooz, Micha and Durin, Bruno and Pioline, Boris and Reichmann, Dori}, - date = {2004}, - journaltitle = {Journal of Cosmology and Astroparticle Physics}, - shortjournal = {J. Cosmol. Astropart. Phys.}, - volume = {2004}, - pages = {002--002}, - issn = {1475-7516}, - doi = {20041012031301}, - abstract = {Misner space, also known as the Lorentzian orbifold \$R\^\{1,1\}/boost\$, is the simplest tree-level solution of string theory with a cosmological singularity. We compute tree-level scattering amplitudes involving twisted states, using operator and current algebra techniques. We find that, due to zero-point quantum fluctuations of the excited modes, twisted strings with a large winding number \$w\$ are fuzzy on a scale \$\textbackslash sqrt\{\textbackslash log w\}\$, which can be much larger than the string scale. Wave functions are smeared by an operator \$\textbackslash exp(\textbackslash Delta(\textbackslash nu) \textbackslash partial\_+ \textbackslash partial\_-)\$ reminiscent of the Moyal-product of non-commutative geometry, which, since \$\textbackslash Delta(\textbackslash nu)\$ is real, modulates the amplitude rather than the phase of the wave function, and is purely gravitational in its origin. We compute the scattering amplitude of two twisted states and one tachyon or graviton, and find a finite result. The scattering amplitude of two twisted and two untwisted states is found to diverge, due to the propagation of intermediate winding strings with vanishing boost momentum. The scattering amplitude of three twisted fields is computed by analytic continuation from three-point amplitudes of states with non-zero \$p\^+\$ in the Nappi-Witten plane wave, and the non-locality of the three-point vertex is found to diverge for certain kinematical configurations. Our results for the three-point amplitudes allow in principle to compute, to leading order, the back-reaction on the metric due to a condensation of coherent winding strings.}, - archivePrefix = {arXiv}, - eprint = {hep-th/0407216}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/berkooz_et_al_2004_closed_strings_in_misner_space8.pdf}, - keywords = {⚠️ Invalid DOI}, - number = {10} + number = {11} } @article{Berkooz:2007:ShortReviewTime, @@ -548,7 +466,7 @@ volume = {171}, pages = {69--87}, issn = {09205632}, - doi = {10.1016/j.nuclphysbps.2007.06.008}, + doi = {10/fnjt32}, abstract = {These lecture notes provide a short review of the status of time dependent backgrounds in String theory, and in particular those that contain space-like singularities. Despite considerable efforts, we do not have yet a full and compelling picture of such backgrounds. We review some of the various attempts to understand these singularities via generalizations of the BKL dynamics, using worldsheet methods and using non-perturbative tools such as the AdS/CFT correspondence and M(atrix) theory. These lecture notes are based on talks given at Cargese 06 and the dead-sea conference 06.}, archivePrefix = {arXiv}, eprint = {0705.2146}, @@ -556,43 +474,6 @@ file = {/home/riccardo/.local/share/zotero/files/berkooz_reichmann_2007_a_short_review_of_time_dependent_solutions_and_space-like_singularities_in.pdf;/home/riccardo/.local/share/zotero/storage/6E7HYPT8/0705.html} } -@article{Bertolini:2006:BraneWorldEffective, - title = {Brane World Effective Actions for {{D}}-Branes with Fluxes}, - author = {Bertolini, Matteo and Billo, Marco and Lerda, Alberto and Morales, Jose F. and Russo, Rodolfo}, - date = {2006}, - journaltitle = {Nuclear Physics B}, - shortjournal = {Nuclear Physics B}, - volume = {743}, - pages = {1--40}, - issn = {05503213}, - doi = {10.1016/j.nuclphysb.2006.02.044}, - abstract = {We develop systematic string techniques to study brane world effective actions for models with magnetized (or equivalently intersecting) D-branes. In particular, we derive the dependence on all NS-NS moduli of the kinetic terms of the chiral matter in a generic non-supersymmetric brane configurations with non-commuting open string fluxes. Near a N=1 supersymmetric point the effective action is consistent with a Fayet-Iliopoulos supersymmetry breaking and the normalization of the scalar kinetic terms is nothing else than the Kahler metric. We also discuss, from a stringy perspective, D and F term breaking mechanisms, and how, in this generic set up, the Kahler metric enters in the physical Yukawa couplings.}, - archivePrefix = {arXiv}, - eprint = {hep-th/0512067}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/bertolini_et_al_2006_brane_world_effective_actions_for_d-branes_with_fluxes5.pdf}, - number = {1-2} -} - -@article{Betzler:2020:ConnectingDualitiesMachine, - title = {Connecting {{Dualities}} and {{Machine Learning}}}, - author = {Betzler, Philip and Krippendorf, Sven}, - date = {2020}, - journaltitle = {Fortschritte der Physik}, - shortjournal = {Fortschr. Phys.}, - volume = {68}, - pages = {2000022}, - issn = {0015-8208, 1521-3978}, - doi = {10.1002/prop.202000022}, - archivePrefix = {arXiv}, - eprint = {2002.05169}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/betzler_krippendorf_2020_connecting_dualities_and_machine_learning2.pdf}, - keywords = {archived}, - langid = {english}, - number = {5} -} - @article{Bianchi:2005:OpenStoryMagnetic, title = {The Open Story of the Magnetic Fluxes}, author = {Bianchi, Massimo and Trevigne, Elisa}, @@ -602,7 +483,7 @@ volume = {2005}, pages = {034--034}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2005/08/034}, + doi = {10/bjnzck}, abstract = {We discuss the effects of oblique internal magnetic fields on the spectrum of type I superstrings compactified on tori. In particular we derive general formulae for the magnetic shifts and multiplicities of open strings connecting D9-branes with arbitrary magnetic fluxes. We discuss the flux induced potential and offer an interpretation of the stabilization of R-R moduli associated to deformations of the complex structure of T\^6 in terms of non-derivative mixing with NS-NS moduli. Finally we briefly comment on how to extract other low energy couplings and generalize our results to toroidal orbifolds and other configurations governed by rational conformal field theories on the worldsheet.}, archivePrefix = {arXiv}, eprint = {hep-th/0502147}, @@ -611,18 +492,6 @@ number = {08} } -@online{Bies:2020:MachineLearningAlgebraic, - title = {Machine {{Learning}} and {{Algebraic Approaches}} towards {{Complete Matter Spectra}} in {{4D F}}-Theory}, - author = {Bies, Martin and Cvetic, Mirjam and Donagi, Ron and Lin, Ling and Liu, Muyang and Ruehle, Fabian}, - date = {2020}, - abstract = {Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d F-theory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. To quantify jumps of these cohomologies, we first generate 1.8 million pairs of line bundles and curves embedded in \$dP\_3\$, for which we compute the cohomologies. A white-box machine learning approach trained on this data provides intuition for jumps due to curve splittings, which we use to construct additional vector-like Higgs-pairs in an F-Theory toy model. We also find that, in order to explain quantitatively the full dataset, further tools from algebraic geometry, in particular Brill--Noether theory, are required. Using these ingredients, we introduce a diagrammatic way to express cohomology jumps across the parameter space of each family of matter curves, which reflects a stratification of the F-theory complex structure moduli space in terms of the vector-like spectrum. Furthermore, these insights provide an algorithmically efficient way to estimate the possible cohomology dimensions across the entire parameter space.}, - archivePrefix = {arXiv}, - eprint = {2007.00009}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/bies_et_al_2020_machine_learning_and_algebraic_approaches_towards_complete_matter_spectra_in_4d2.pdf;/home/riccardo/.local/share/zotero/storage/DZLMDN6C/2007.html}, - keywords = {⛔ No DOI found} -} - @article{Bizet:2020:TestingSwamplandConjectures, title = {Testing Swampland Conjectures with Machine Learning}, author = {Bizet, Nana Cabo and Damian, Cesar and Loaiza-Brito, Oscar and Mayorga Peña, Damián Kaloni and Montañez-Barrera, J. A.}, @@ -632,7 +501,7 @@ volume = {80}, pages = {766}, issn = {1434-6044, 1434-6052}, - doi = {10.1140/epjc/s10052-020-8332-9}, + doi = {10/ghf4ns}, abstract = {Abstract We consider Type IIB compactifications on an isotropic torus \$\$T\^6\$\$ T 6 threaded by geometric and non geometric fluxes. For this particular setup we apply supervised machine learning techniques, namely an artificial neural network coupled to a genetic algorithm, in order to obtain more than sixty thousand flux configurations yielding to a scalar potential with at least one critical point. We observe that both stable AdS vacua with large moduli masses and small vacuum energy as well as unstable dS vacua with small tachyonic mass and large energy are absent, in accordance to the refined de Sitter conjecture. Moreover, by considering a hierarchy among fluxes, we observe that perturbative solutions with small values for the vacuum energy and moduli masses are favored, as well as scenarios in which the lightest modulus mass is much smaller than the corresponding AdS vacuum scale. Finally we apply some results on random matrix theory to conclude that the most probable mass spectrum derived from this string setup is that satisfying the Refined de Sitter and AdS scale conjectures.}, archivePrefix = {arXiv}, eprint = {2006.07290}, @@ -651,7 +520,7 @@ volume = {859}, pages = {299--320}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2012.02.009}, + doi = {10/gg66ng}, archivePrefix = {arXiv}, eprint = {1107.4321}, eprinttype = {arxiv}, @@ -670,7 +539,7 @@ volume = {713}, pages = {83--135}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2005.02.005}, + doi = {10/dxmsqx}, archivePrefix = {arXiv}, eprint = {hep-th/0411173}, eprinttype = {arxiv}, @@ -688,7 +557,7 @@ volume = {445}, pages = {1--193}, issn = {03701573}, - doi = {10.1016/j.physrep.2007.04.003}, + doi = {10/dthp8q}, abstract = {This review article provides a pedagogical introduction into various classes of chiral string compactifications to four dimensions with D-branes and fluxes. The main concern is to provide all necessary technical tools to explicitly construct four-dimensional orientifold vacua, with the final aim to come as close as possible to the supersymmetric Standard Model. Furthermore, we outline the available methods to derive the resulting four-dimensional effective action. Finally, we summarize recent attempts to address the string vacuum problem via the statistical approach to D-brane models.}, archivePrefix = {arXiv}, eprint = {hep-th/0610327}, @@ -702,28 +571,15 @@ author = {Blumenhagen, Ralph and Plauschinn, Erik}, date = {2009}, volume = {779}, - publisher = {{Springer Berlin Heidelberg}}, + publisher = {{Springer}}, location = {{Berlin, Heidelberg}}, - doi = {10.1007/978-3-642-00450-6}, + url = {http://link.springer.com/10.1007/978-3-642-00450-6}, file = {/home/riccardo/.local/share/zotero/files/blumenhagen_plauschinn_2009_introduction_to_conformal_field_theory.pdf}, - isbn = {978-3-642-00449-0 978-3-642-00450-6}, + isbn = {978-3-642-00449-0}, langid = {english}, series = {Lecture {{Notes}} in {{Physics}}} } -@book{Blumenhagen:2013:BasicConceptsString, - title = {Basic {{Concepts}} of {{String Theory}}}, - author = {Blumenhagen, Ralph and Lüst, Dieter and Theisen, Stefan}, - date = {2013}, - publisher = {{Springer Berlin Heidelberg}}, - location = {{Berlin, Heidelberg}}, - doi = {10.1007/978-3-642-29497-6}, - file = {/home/riccardo/.local/share/zotero/files/blumenhagen_et_al_2013_basic_concepts_of_string_theory.pdf}, - isbn = {978-3-642-29496-9 978-3-642-29497-6}, - langid = {english}, - series = {Theoretical and {{Mathematical Physics}}} -} - @article{Bousso:2000:QuantizationFourformFluxes, title = {Quantization of {{Four}}-Form {{Fluxes}} and {{Dynamical Neutralization}} of the {{Cosmological Constant}}}, author = {Bousso, Raphael and Polchinski, Joseph}, @@ -733,7 +589,7 @@ volume = {2000}, pages = {006--006}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2000/06/006}, + doi = {10/fwrxdr}, abstract = {A four-form gauge flux makes a variable contribution to the cosmological constant. This has often been assumed to take continuous values, but we argue that it has a generalized Dirac quantization condition. For a single flux the steps are much larger than the observational limit, but we show that with multiple fluxes the allowed values can form a sufficiently dense `discretuum'. Multiple fluxes generally arise in M theory compactifications on manifolds with non-trivial three-cycles. In theories with large extra dimensions a few four-forms suffice; otherwise of order 100 are needed. Starting from generic initial conditions, the repeated nucleation of membranes dynamically generates regions with a cosmological constant in the observational range. Entropy and density perturbations can be produced.}, archivePrefix = {arXiv}, eprint = {hep-th/0004134}, @@ -744,13 +600,13 @@ @inproceedings{Brennan:2018:StringLandscapeSwampland, title = {The {{String Landscape}}, the {{Swampland}}, and the {{Missing Corner}}}, - booktitle = {Proceedings of {{Theoretical Advanced Study Institute Summer School}} 2017 "{{Physics}} at the {{Fundamental Frontier}}" — {{PoS}}({{TASI2017}})}, + booktitle = {Proceedings of {{Theoretical Advanced Study Institute Summer School}} 2017 "{{Physics}} at the {{Fundamental Frontier}}"}, author = {Brennan, Theodore Daniel and Carta, Federico and Vafa, Cumrun}, date = {2018}, pages = {015}, publisher = {{Sissa Medialab}}, location = {{Boulder, Colorado}}, - doi = {10.22323/1.305.0015}, + doi = {10/ghf4nt}, archivePrefix = {arXiv}, eprint = {1711.00864}, eprinttype = {arxiv}, @@ -769,7 +625,7 @@ volume = {68}, pages = {1900087}, issn = {0015-8208, 1521-3978}, - doi = {10.1002/prop.201900087}, + doi = {10/gg66m6}, archivePrefix = {arXiv}, eprint = {1906.08730}, eprinttype = {arxiv}, @@ -779,23 +635,6 @@ number = {1} } -@article{Brown:1988:NeutralizationCosmologicalConstant, - title = {Neutralization of the Cosmological Constant by Membrane Creation}, - author = {Brown, David J. and Teitelboim, Claudio}, - date = {1988}, - journaltitle = {Nuclear Physics B}, - shortjournal = {Nuclear Physics B}, - volume = {297}, - pages = {787--836}, - issn = {05503213}, - doi = {10.1016/0550-3213(88)90559-7}, - annotation = {http://web.archive.org/web/20200904101758/https://linkinghub.elsevier.com/retrieve/pii/0550321388905597}, - file = {/home/riccardo/.local/share/zotero/files/brown_teitelboim_1988_neutralization_of_the_cosmological_constant_by_membrane_creation.pdf}, - keywords = {archived}, - langid = {english}, - number = {4} -} - @article{Bull:2018:MachineLearningCICY, title = {Machine Learning {{CICY}} Threefolds}, author = {Bull, Kieran and He, Yang-Hui and Jejjala, Vishnu and Mishra, Challenger}, @@ -805,7 +644,7 @@ volume = {785}, pages = {65--72}, issn = {03702693}, - doi = {10.1016/j.physletb.2018.08.008}, + doi = {10/gfm446}, archivePrefix = {arXiv}, eprint = {1806.03121}, eprinttype = {arxiv}, @@ -823,7 +662,7 @@ volume = {795}, pages = {700--706}, issn = {03702693}, - doi = {10.1016/j.physletb.2019.06.067}, + doi = {10/gg66m5}, archivePrefix = {arXiv}, eprint = {1903.03113}, eprinttype = {arxiv}, @@ -841,8 +680,7 @@ volume = {355}, pages = {689--711}, issn = {05503213}, - doi = {10.1016/0550-3213(91)90491-F}, - annotation = {http://web.archive.org/web/20200909161147/https://linkinghub.elsevier.com/retrieve/pii/055032139190491F}, + doi = {10/c56dxj}, file = {/home/riccardo/.local/share/zotero/files/burwick_et_al_1991_general_yukawa_couplings_of_strings_on_orbifolds.pdf}, keywords = {archived}, langid = {english}, @@ -859,12 +697,12 @@ @inproceedings{Calabi:1957:KahlerManifoldsVanishing, title = {On {{Kähler}} Manifolds with Vanishing Canonical Class}, - booktitle = {Algebraic Geometry and Topology. {{A}} Symposium in Honor of {{S}}. {{Lefschetz}}}, + booktitle = {Algebraic Geometry and Topology. {{A}} Symposium in Honor of {{S}}. {{Lefschetz}}.}, author = {Calabi, Eugenio}, date = {1957}, volume = {12}, pages = {78--89}, - doi = {10.1515/9781400879915-006}, + doi = {10/ghf4nv}, file = {/home/riccardo/.local/share/zotero/files/calabi_1957_on_kähler_manifolds_with_vanishing_canonical_class.pdf} } @@ -877,7 +715,7 @@ volume = {258}, pages = {46--74}, issn = {05503213}, - doi = {10.1016/0550-3213(85)90602-9}, + doi = {10/bxjjzx}, abstract = {We study candidate vacuum configurations in ten-dimensional O(32) and E8 × E8 supergravity and superstring theory that have unbroken N = 1 supersymmetry in four dimensions. This condition permits only a few possibilities, all of which have vanishing cosmological constant. In the E8 × E8 case, one of these possibilities leads to a model that in four dimensions has an E6 gauge group with four standard generations of fermions.}, file = {/home/riccardo/.local/share/zotero/files/candelas_et_al_1985_vacuum_configurations_for_superstrings.pdf}, keywords = {archived}, @@ -893,8 +731,7 @@ volume = {298}, pages = {493--525}, issn = {05503213}, - doi = {10.1016/0550-3213(88)90352-5}, - annotation = {http://web.archive.org/web/20201007122008/https://linkinghub.elsevier.com/retrieve/pii/0550321388903525}, + doi = {10/cbx253}, file = {/home/riccardo/.local/share/zotero/files/candelas_et_al_1988_complete_intersection_calabi-yau_manifolds3.pdf}, keywords = {archived}, langid = {english}, @@ -922,7 +759,7 @@ volume = {2017}, pages = {157}, issn = {1029-8479}, - doi = {10.1007/JHEP09(2017)157}, + doi = {10/gb4szm}, archivePrefix = {arXiv}, eprint = {1707.00655}, eprinttype = {arxiv}, @@ -931,24 +768,6 @@ number = {9} } -@article{Carleo:2019:MachineLearningPhysical, - title = {Machine Learning and the Physical Sciences}, - author = {Carleo, Giuseppe and Cirac, Ignacio and Cranmer, Kyle and Daudet, Laurent and Schuld, Maria and Tishby, Naftali and Vogt-Maranto, Leslie and Zdeborová, Lenka}, - date = {2019}, - journaltitle = {Reviews of Modern Physics}, - shortjournal = {Rev. Mod. Phys.}, - volume = {91}, - pages = {045002}, - issn = {0034-6861, 1539-0756}, - doi = {10.1103/RevModPhys.91.045002}, - abstract = {Machine learning encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. We review in a selective way the recent research on the interface between machine learning and physical sciences. This includes conceptual developments in machine learning (ML) motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross-fertilization between the two fields. After giving basic notion of machine learning methods and principles, we describe examples of how statistical physics is used to understand methods in ML. We then move to describe applications of ML methods in particle physics and cosmology, quantum many body physics, quantum computing, and chemical and material physics. We also highlight research and development into novel computing architectures aimed at accelerating ML. In each of the sections we describe recent successes as well as domain-specific methodology and challenges.}, - archivePrefix = {arXiv}, - eprint = {1903.10563}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/carleo_et_al_2019_machine_learning_and_the_physical_sciences2.pdf;/home/riccardo/.local/share/zotero/storage/IVAHE4BQ/1903.html}, - number = {4} -} - @article{Caruana:1997:MultitaskLearning, title = {Multitask Learning}, author = {Caruana, Rich}, @@ -956,8 +775,7 @@ journaltitle = {Machine learning}, volume = {28}, pages = {41--75}, - publisher = {{Springer}}, - doi = {10.1023/A:1007379606734}, + doi = {10/d3gsgj}, file = {/home/riccardo/.local/share/zotero/files/caruana_1997_multitask_learning3.pdf}, number = {1} } @@ -981,7 +799,7 @@ volume = {69}, pages = {095011}, issn = {1550-7998, 1550-2368}, - doi = {10.1103/PhysRevD.69.095011}, + doi = {10/dbfm3j}, archivePrefix = {arXiv}, eprint = {hep-ph/0309169}, eprinttype = {arxiv}, @@ -1000,7 +818,7 @@ volume = {665}, pages = {267--270}, issn = {03702693}, - doi = {10.1016/j.physletb.2008.06.024}, + doi = {10/b25m9j}, abstract = {We briefly describe a three-family intersecting D6-brane model in Type IIA theory on the T\^6/(Z\_2 x Z\_2) orientifold with a realistic phenomenology. In this model, the gauge symmetry can be broken down to the Standard Model (SM) gauge symmetry close to the string scale, and the gauge coupling unification can be achieved. We calculate the supersymmetry breaking soft terms, and the corresponding low energy supersymmetric particle spectrum, which may be tested at the Large Hadron Collider (LHC). The observed dark matter density may also be generated. Finally, we can explain the SM quark masses and CKM mixings, and the tau lepton mass. The neutrino masses and mixings may be generated via the seesaw mechanism as well.}, archivePrefix = {arXiv}, eprint = {hep-th/0703280}, @@ -1018,7 +836,7 @@ volume = {77}, pages = {125023}, issn = {1550-7998, 1550-2368}, - doi = {10.1103/PhysRevD.77.125023}, + doi = {10/c3gb98}, abstract = {We study the possible phenomenology of a three-family Pati-Salam model constructed from intersecting D6-branes in Type IIA string theory on the T\^6/(Z2 x Z2) orientifold with some desirable semi-realistic features. In the model, tree-level gauge coupling unification is achieved automatically at the string scale, and the gauge symmetry may be broken to the Standard Model (SM) close to the string scale. The small number of extra chiral exotic states in the model may be decoupled via the Higgs mechanism and strong dynamics. We calculate the possible supersymmetry breaking soft terms and the corresponding low-energy supersymmetric particle spectra which may potentially be tested at the Large Hadron Collider (LHC). We find that for the viable regions of the parameter space the lightest CP-even Higgs boson mass usually satisfies m\_H {$<$} 120 GeV, and the observed dark matter density may be generated. Finally, we find that it is possible to obtain correct SM quark masses and mixings, and the tau lepton mass at the unification scale. Additionally, neutrino masses and mixings may be generated via the seesaw mechanism. Mechanisms to stabilize the open and closed-string moduli, which are necessary for the model to be truly viable and to make definite predictions are discussed.}, archivePrefix = {arXiv}, eprint = {0711.0396}, @@ -1027,27 +845,14 @@ number = {12} } -@online{Chen:2020:MachineLearningEtudes, - title = {Machine {{Learning Etudes}} in {{Conformal Field Theories}}}, - author = {Chen, Heng-Yu and He, Yang-Hui and Lal, Shailesh and Zaz, M. Zaid}, - date = {2020}, - abstract = {We demonstrate that various aspects of Conformal Field Theory are amenable to machine learning. Relatively modest feed-forward neural networks are able to distinguish between scale and conformal invariance of a three-point function and identify a crossing-symmetric four-point function to nearly a hundred percent accuracy. Furthermore, neural networks are also able to identify conformal blocks appearing in a putative CFT four-point function and predict the values of the corresponding OPE coefficients. Neural networks also successfully classify primary operators by their quantum numbers under discrete symmetries in the CFT from examining OPE data. We also demonstrate that neural networks are able to learn the available OPE data for scalar correlation function in the 3d Ising model and predict the twists of higher-spin operators that appear in scalar OPE channels by regression.}, - archivePrefix = {arXiv}, - eprint = {2006.16114}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/chen_et_al_2020_machine_learning_etudes_in_conformal_field_theories.pdf;/home/riccardo/.local/share/zotero/storage/PGR2JCWQ/2006.html}, - keywords = {⛔ No DOI found} -} - @book{Chollet:2018:DeepLearningPython, title = {Deep {{Learning}} with {{Python}}}, author = {Chollet, François}, date = {2018}, - publisher = {{Manning Publications Co}}, + publisher = {{Manning Publications Co.}}, location = {{Shelter Island, New York}}, - url = {https://www.manning.com/books/deep-learning-with-python#toc}, + url = {https://www.manning.com/books/deep-learning-with-python}, abstract = {Deep Learning with Python introduces the field of deep learning using the Python language and the powerful Keras library. Written by Keras creator and Google AI researcher François Chollet, this book builds your understanding through intuitive explanations and practical examples. You'll explore challenging concepts and practice with applications in computer vision, natural-language processing, and generative models. By the time you finish, you'll have the knowledge and hands-on skills to apply deep learning in your own projects.}, - annotation = {OCLC: ocn982650571}, file = {/home/riccardo/.local/share/zotero/files/chollet_2018_deep_learning_with_python.pdf}, isbn = {978-1-61729-443-3}, langid = {english}, @@ -1075,7 +880,7 @@ volume = {2019}, pages = {45}, issn = {1029-8479}, - doi = {10.1007/JHEP11(2019)045}, + doi = {10/ghf4nw}, archivePrefix = {arXiv}, eprint = {1907.10072}, eprinttype = {arxiv}, @@ -1084,42 +889,6 @@ number = {11} } -@article{Cole:2019:TopologicalDataAnalysis, - title = {Topological Data Analysis for the String Landscape}, - author = {Cole, Alex and Shiu, Gary}, - date = {2019}, - journaltitle = {Journal of High Energy Physics}, - shortjournal = {J. High Energ. Phys.}, - volume = {2019}, - pages = {54}, - issn = {1029-8479}, - doi = {10.1007/JHEP03(2019)054}, - archivePrefix = {arXiv}, - eprint = {1812.06960}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/cole_shiu_2019_topological_data_analysis_for_the_string_landscape2.pdf}, - langid = {english}, - number = {3} -} - -@article{Comsa:2019:SupergravityMagicMachine, - title = {{{SO}}(8) Supergravity and the Magic of Machine Learning}, - author = {Comsa, Iulia M. and Firsching, Moritz and Fischbacher, Thomas}, - date = {2019}, - journaltitle = {Journal of High Energy Physics}, - shortjournal = {J. High Energ. Phys.}, - volume = {2019}, - pages = {57}, - issn = {1029-8479}, - doi = {10.1007/JHEP08(2019)057}, - archivePrefix = {arXiv}, - eprint = {1906.00207}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/comsa_et_al_2019_so(8)_supergravity_and_the_magic_of_machine_learning3.pdf}, - langid = {english}, - number = {8} -} - @article{Constantin:2019:CountingStringTheory, title = {Counting String Theory Standard Models}, author = {Constantin, Andrei and He, Yang-Hui and Lukas, Andre}, @@ -1129,7 +898,7 @@ volume = {792}, pages = {258--262}, issn = {03702693}, - doi = {10.1016/j.physletb.2019.03.048}, + doi = {10/ghf4nx}, archivePrefix = {arXiv}, eprint = {1810.00444}, eprinttype = {arxiv}, @@ -1147,7 +916,7 @@ volume = {66}, pages = {066001}, issn = {0556-2821, 1089-4918}, - doi = {10.1103/PhysRevD.66.066001}, + doi = {10/c4nfnn}, abstract = {We consider new cosmological solutions with a collapsing, an intermediate and an expanding phase. The boundary between the expanding (collapsing) phase and the intermediate phase is seen by comoving observers as a cosmological past (future) horizon. The solutions are naturally embedded in string and M-theory. In the particular case of a two-dimensional cosmology, space-time is flat with an identification under boost and translation transformations. We consider the corresponding string theory orbifold and calculate the modular invariant one-loop partition function. In this case there is a strong parallel with the BTZ black hole. The higher dimensional cosmologies have a time-like curvature singularity in the intermediate region. In some cases the string coupling can be made small throughout all of space-time but string corrections become important at the singularity. This happens where string winding modes become light which could resolve the singularity. The new proposed space-time casual structure could have implications for cosmology, independently of string theory.}, archivePrefix = {arXiv}, eprint = {hep-th/0203031}, @@ -1157,7 +926,6 @@ } @article{Cornalba:2004:TimedependentOrbifoldsString, - ids = {Cornalba:2004:TimeDependentOrbifolds}, title = {Time-Dependent Orbifolds and String Cosmology}, author = {Cornalba, Lorenzo and Costa, Miguel S.}, date = {2004}, @@ -1165,9 +933,8 @@ volume = {52}, pages = {145--199}, issn = {00158208}, - doi = {10.1002/prop.200310123}, + doi = {10/brv6jj}, abstract = {In these lectures, we review the physics of time-dependent orbifolds of string theory, with particular attention to orbifolds of three-dimensional Minkowski space. We discuss the propagation of free particles in the orbifold geometries, together with their interactions. We address the issue of stability of these string vacua and the difficulties in defining a consistent perturbation theory, pointing to possible solutions. In particular, it is shown that resumming part of the perturbative expansion gives finite amplitudes. Finally we discuss the duality of some orbifold models with the physics of orientifold planes, and we describe cosmological models based on the dynamics of these orientifolds.}, - annotation = {ZSCC: 0000143}, archivePrefix = {arXiv}, eprint = {hep-th/0310099}, eprinttype = {arxiv}, @@ -1188,7 +955,6 @@ } @article{Craps:2002:StringPropagationPresence, - ids = {Craps:2002:StringPropagationPresencea}, title = {String {{Propagation}} in the {{Presence}} of {{Cosmological Singularities}}}, author = {Craps, Ben and Kutasov, David and Rajesh, Govindan}, date = {2002}, @@ -1197,18 +963,16 @@ volume = {2002}, pages = {053--053}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2002/06/053}, + doi = {10/cjdtw7}, abstract = {We study string propagation in a spacetime with positive cosmological constant, which includes a circle whose radius approaches a finite value as |t|\textbackslash to\textbackslash infty, and goes to zero at t=0. Near this cosmological singularity, the spacetime looks like R\^\{1,1\}/Z. In string theory, this spacetime must be extended by including four additional regions, two of which are compact. The other two introduce new asymptotic regions, corresponding to early and late times, respectively. States of quantum fields in this spacetime are defined in the tensor product of the two Hilbert spaces corresponding to the early time asymptotic regions, and the S-matrix describes the evolution of such states to states in the tensor product of the two late time asymptotic regions. We show that string theory provides a unique continuation of wavefunctions past the cosmological singularities, and allows one to compute the S-matrix. The incoming vacuum evolves into an outgoing state with particles. We also discuss instabilities of asymptotically timelike linear dilaton spacetimes, and the question of holography in such spaces. Finally, we briefly comment on the relation of our results to recent discussions of de Sitter space.}, archivePrefix = {arXiv}, eprint = {hep-th/0205101}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/craps_et_al_2002_string_propagation_in_the_presence_of_cosmological_singularities.pdf}, - issue = {06}, - number = {EFI-02-77} + number = {06} } @article{Craps:2006:BigBangModels, - ids = {Craps:2006:BigBangModelsa}, title = {Big {{Bang Models}} in {{String Theory}}}, author = {Craps, Ben}, date = {2006}, @@ -1217,7 +981,7 @@ volume = {23}, pages = {S849-S881}, issn = {0264-9381, 1361-6382}, - doi = {10.1088/0264-9381/23/21/S01}, + doi = {10/cx8s3s}, abstract = {These proceedings are based on lectures delivered at the "RTN Winter School on Strings, Supergravity and Gauge Theories", CERN, January 16 - January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures start with a brief introduction to spacetime singularities and the string theory resolution of certain static singularities. Then they discuss attempts to resolve cosmological singularities in string theory, mainly focusing on two specific examples: the Milne orbifold and the matrix big bang.}, archivePrefix = {arXiv}, eprint = {hep-th/0605199}, @@ -1235,7 +999,7 @@ volume = {2003}, pages = {038--038}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2003/07/038}, + doi = {10/bpp94m}, abstract = {We compute the Yukawa couplings among chiral fields in toroidal Type II compactifications with wrapping D6-branes intersecting at angles. Those models can yield realistic standard model spectrum living at the intersections. The Yukawa couplings depend both on the Kahler and open string moduli but not on the complex structure. They arise from worldsheet instanton corrections and are found to be given by products of complex Jacobi theta functions with characteristics. The Yukawa couplings for a particular intersecting brane configuration yielding the chiral spectrum of the MSSM are computed as an example. We also show how our methods can be extended to compute Yukawa couplings on certain classes of elliptically fibered CY manifolds which are mirror to complex cones over del Pezzo surfaces. We find that the Yukawa couplings in intersecting D6-brane models have a mathematical interpretation in the context of homological mirror symmetry. In particular, the computation of such Yukawa couplings is related to the construction of Fukaya's category in a generic symplectic manifold.}, archivePrefix = {arXiv}, eprint = {hep-th/0302105}, @@ -1253,7 +1017,7 @@ volume = {2010}, pages = {5}, issn = {1029-8479}, - doi = {10.1007/JHEP01(2010)005}, + doi = {10/dg2zz6}, abstract = {We study in detail the system of D6 branes and euclidean D2-brane instantons intersecting at angles in type IIA string theory. We find that in the absence of orientifolds the system does not contribute to the low energy superpotential, in agreement with expectations based on effective field theory arguments. We also comment on the implications of our results for dual string theory pictures.}, archivePrefix = {arXiv}, eprint = {0905.1694}, @@ -1271,7 +1035,7 @@ volume = {674}, pages = {80--170}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2003.09.020}, + doi = {10/cwvfg9}, abstract = {The non-compact CFT of a class of NS-supported pp-wave backgrounds is solved exactly. The associated tree-level covariant string scattering amplitudes are calculated. The S-matrix elements are well-defined, dual but not analytic as a function of \$p\^+\$. They have poles corresponding to physical intermediate states with \$p\^+\textbackslash not =0\$ and logarithmic branch cuts due to on-shell exchange of spectral-flow images of \$p\^+=0\$ states. When \$\textbackslash mu\textbackslash to 0\$ a smooth flat space limit is obtained. The \$\textbackslash mu\textbackslash to\textbackslash infty\$ limit, unlike the case of RR-supported pp-waves, gives again a flat space theory.}, archivePrefix = {arXiv}, eprint = {hep-th/0305081}, @@ -1280,24 +1044,6 @@ number = {1-2} } -@article{DAppollonio:2005:DbranesBCFTHppwave, - title = {D-Branes and {{BCFT}} in {{Hpp}}-Wave Backgrounds}, - author = {D'Appollonio, Giuseppe and Kiritsis, Elias}, - date = {2005}, - journaltitle = {Nuclear Physics B}, - shortjournal = {Nuclear Physics B}, - volume = {712}, - pages = {433--512}, - issn = {05503213}, - doi = {10.1016/j.nuclphysb.2005.01.020}, - abstract = {In this paper we study two classes of symmetric D-branes in the Nappi-Witten gravitational wave, namely D2 and \$S 1\$ branes. We solve the sewing constraints and determine the bulk-boundary couplings and the boundary three-point couplings. For the D2 brane our solution gives the first explicit results for the structure constants of the twisted symmetric branes in a WZW model. We also compute the boundary four-point functions, providing examples of open string four-point amplitudes in a curved background. We finally discuss the annulus amplitudes, the relation with branes in \$AdS\_3\$ and in \$S\^3\$ and the analogy between the open string couplings in the \$H\_4\$ model and the couplings for magnetized and intersecting branes.}, - archivePrefix = {arXiv}, - eprint = {hep-th/0410269}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/d'appollonio_kiritsis_2005_d-branes_and_bcft_in_hpp-wave_backgrounds5.pdf}, - number = {3} -} - @article{David:2000:TachyonCondensationD0, title = {Tachyon Condensation in the {{D0}}/{{D4}} System}, author = {David, Justin R.}, @@ -1326,7 +1072,7 @@ volume = {2001}, pages = {009--009}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2001/07/009}, + doi = {10/fb5m3w}, abstract = {It has been recently proposed that the background independent open superstring field theory action is given by the disc partition function with all possible open string operators inserted at the boundary of the disc. We use this proposal to study tachyon condensation in the D0-D2 system. We evaluate the disc partition function for the D0-D2 system in presence of a large Neveu-Schwarz B-field using perturbation theory. This perturbative expansion of the disc partition function makes sense as the boundary tachyon operator for the large Neveu-Schwarz B-field is almost marginal. We find that the mass defect for the formation of the D0-D2 bound state agrees exactly with the expected result in the large B-field limit.}, archivePrefix = {arXiv}, eprint = {hep-th/0012089}, @@ -1335,39 +1081,6 @@ number = {07} } -@article{David:2002:ClosedStringTachyon, - title = {Closed {{String Tachyon Condensation}} on {{Twisted Circles}}}, - author = {David, Justin R. and Gutperle, Michael and Headrick, Matthew and Minwalla, Shiraz}, - date = {2002}, - journaltitle = {Journal of High Energy Physics}, - shortjournal = {J. High Energy Phys.}, - volume = {2002}, - pages = {041--041}, - issn = {1029-8479}, - doi = {10.1088/1126-6708/2002/02/041}, - abstract = {We study IIA/B string theory compactified on twisted circles. These models possess closed string tachyons and reduce to type 0B/A theory in a special limit. Using methods of gauged linear sigma models and mirror symmetry we construct a conformal field theory which interpolates between these models and flat space via an auxiliary Liouville direction. Interpreting motion in the Liouville direction as renormalization group flow, we argue that the end point of tachyon condensation in all these models (including 0B/A theory) is supersymmetric type II theory. We also find a zero-slope limit of these models which is best described in a T-dual picture as a type II NS-NS fluxbrane. In this limit tachyon condensation is an interesting and well posed problem in supergravity. We explicitly determine the tachyon as a fluctuation of supergravity fields, and perform a rudimentary numerical analysis of the relevant flows.}, - archivePrefix = {arXiv}, - eprint = {hep-th/0111212}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/david_et_al_2002_closed_string_tachyon_condensation_on_twisted_circles5.pdf}, - number = {02} -} - -@article{DellaSelva:1970:SimpleExpressionSciuto, - title = {A Simple Expression for the {{Sciuto}} Three-Reggeon Vertex-Generating Duality}, - author = {Della Selva, Angelo and Saito, Satoru}, - date = {1970}, - journaltitle = {Lettere al Nuovo Cimento}, - shortjournal = {Lett. Nuovo Cimento}, - volume = {4}, - pages = {689--692}, - issn = {0375-930X, 1827-613X}, - doi = {10.1007/BF02755329}, - file = {/home/riccardo/.local/share/zotero/files/selva_saito_1970_a_simple_expression_for_the_sciuto_three-reggeon_vertex-generating_duality.pdf}, - langid = {english}, - number = {15} -} - @article{Denef:2007:ComputationalComplexityLandscape, title = {Computational Complexity of the Landscape: {{Part I}}}, shorttitle = {Computational Complexity of the Landscape}, @@ -1378,7 +1091,7 @@ volume = {322}, pages = {1096--1142}, issn = {00034916}, - doi = {10.1016/j.aop.2006.07.013}, + doi = {10/bp2wbs}, archivePrefix = {arXiv}, eprint = {hep-th/0602072}, eprinttype = {arxiv}, @@ -1397,7 +1110,7 @@ volume = {347}, pages = {651--686}, issn = {05503213}, - doi = {10.1016/0550-3213(90)90379-R}, + doi = {10/ctk5bp}, file = {/home/riccardo/.local/share/zotero/files/di_bartolomeo_et_al_1990_general_properties_of_vertices_with_two_ramond_or_twisted_states4.pdf}, keywords = {archived}, langid = {english}, @@ -1408,11 +1121,11 @@ title = {Conformal {{Field Theory}}}, author = {Di Francesco, Philippe and Mathieu, Pierre and Sénéchal, David}, date = {1997}, - publisher = {{Springer New York}}, + publisher = {{Springer}}, location = {{New York}}, - doi = {10.1007/978-1-4612-2256-9}, + url = {http://link.springer.com/10.1007/978-1-4612-2256-9}, file = {/home/riccardo/.local/share/zotero/files/di_francesco_et_al_1997_conformal_field_theory.pdf}, - isbn = {978-1-4612-7475-9 978-1-4612-2256-9}, + isbn = {978-1-4612-7475-9}, langid = {english}, series = {Graduate {{Texts}} in {{Contemporary Physics}}} } @@ -1426,7 +1139,7 @@ volume = {609}, pages = {408--417}, issn = {03702693}, - doi = {10.1016/j.physletb.2004.04.094}, + doi = {10/frz278}, archivePrefix = {arXiv}, eprint = {hep-th/0403196}, eprinttype = {arxiv}, @@ -1436,25 +1149,6 @@ number = {3-4} } -@article{Dijkstra:2005:SupersymmetricStandardModel, - title = {Supersymmetric Standard Model Spectra from {{RCFT}} Orientifolds}, - author = {Dijkstra, T. P. T. and Huiszoon, Lennaert R. and Schellekens, A. N.}, - date = {2005}, - journaltitle = {Nuclear Physics B}, - shortjournal = {Nuclear Physics B}, - volume = {710}, - pages = {3--57}, - issn = {05503213}, - doi = {10.1016/j.nuclphysb.2004.12.032}, - archivePrefix = {arXiv}, - eprint = {hep-th/0411129}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/dijkstra_et_al_2005_supersymmetric_standard_model_spectra_from_rcft_orientifolds.pdf}, - keywords = {archived}, - langid = {english}, - number = {1-2} -} - @article{DiVecchia:1990:VertexIncludingEmission, title = {A Vertex Including Emission of Spin Fields}, author = {Di Vecchia, Paolo and Madsen, R. and Hornfeck, Klaus and Roland, Kaj}, @@ -1464,7 +1158,7 @@ volume = {235}, pages = {63--70}, issn = {03702693}, - doi = {10.1016/0370-2693(90)90098-Q}, + doi = {10/fr3zhk}, file = {/home/riccardo/.local/share/zotero/files/di_vecchia_et_al_1990_a_vertex_including_emission_of_spin_fields4.pdf}, keywords = {archived}, langid = {english}, @@ -1479,7 +1173,7 @@ volume = {507}, pages = {259--276}, issn = {05503213}, - doi = {10.1016/s0550-3213(97)00576-2}, + doi = {10/bjkrq3}, abstract = {We show that the boundary state description of a Dp-brane is strictly related to the corresponding classical solution of the low-energy string effective action. By projecting the boundary state on the massless states of the closed string we obtain the tension, the R-R charge and the large distance behavior of the classical solution. We discuss both the case of a single D-brane and that of bound states of two D-branes. We also show that in the R-R sector the boundary state, written in a picture which treats asymmetrically the left and right components, directly yields the R-R gauge potentials.}, archivePrefix = {arXiv}, eprint = {hep-th/9707068}, @@ -1490,14 +1184,15 @@ @inproceedings{DiVecchia:1999:DbranesStringTheory, title = {D-Branes in String Theory {{II}}}, - booktitle = {{{YITP}} Workshop on Developments in Superstring and {{M}} Theory}, + booktitle = {{{YITP}} Workshop on Developments in Superstring and {{M}}-Theory}, author = {Di Vecchia, Paolo and Liccardo, Antonella}, date = {1999}, pages = {7--48}, archivePrefix = {arXiv}, eprint = {hep-th/9912275}, eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/di_vecchia_liccardo_1999_d-branes_in_string_theory.pdf} + file = {/home/riccardo/.local/share/zotero/files/di_vecchia_liccardo_1999_d-branes_in_string_theory.pdf}, + keywords = {⛔ No DOI found} } @article{DiVecchia:2000:BranesStringTheory, @@ -1508,7 +1203,7 @@ journaltitle = {NATO Sci. Ser. C}, volume = {556}, pages = {1--60}, - doi = {10.1007/978-94-011-4303-5_1}, + doi = {10/gf66cb}, archivePrefix = {arXiv}, eprint = {hep-th/9912161}, eprinttype = {arxiv}, @@ -1518,18 +1213,18 @@ @inproceedings{DiVecchia:2006:BoundaryStateMagnetized, title = {Boundary {{State}} for {{Magnetized D9 Branes}} and {{One}}-{{Loop Calculation}}}, - booktitle = {Sense of {{Beauty}} in {{Physics}}: {{Miniconference}} in {{Honor}} of {{Adriano Di Giacomo}} on His 70th {{Birthday}}}, + booktitle = {Proceedings of {{Sense}} of {{Beauty}} in {{Physics}}: {{Miniconference}} in {{Honor}} of {{Adriano Di Giacomo}} on His 70th {{Birthday}}}, author = {Di Vecchia, Paolo and Liccardo, Antonella and Marotta, Raffaele and Pezzella, Franco and Pesando, Igor}, date = {2006}, abstract = {We construct the boundary state describing magnetized D9 branes in R\^\{3,1\} x T\^6 and we use it to compute the annulus and Moebius amplitudes. We derive from them, by using open/closed string duality, the number of Landau levels on the torus T\^d.}, archivePrefix = {arXiv}, eprint = {hep-th/0601067}, eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/di_vecchia_et_al_2006_boundary_state_for_magnetized_d9_branes_and_one-loop_calculation.pdf} + file = {/home/riccardo/.local/share/zotero/files/di_vecchia_et_al_2006_boundary_state_for_magnetized_d9_branes_and_one-loop_calculation.pdf}, + keywords = {⛔ No DOI found} } @article{DiVecchia:2007:WrappedMagnetizedBranes, - ids = {DiVecchia:2007:WrappedMagnetizedBranesa}, title = {Wrapped Magnetized Branes: Two Alternative Descriptions?}, author = {Di Vecchia, Paolo and Liccardo, Antonella and Marotta, Raffaele and Pezzella, Franco and Pesando, Igor}, date = {2007}, @@ -1537,16 +1232,13 @@ volume = {2007}, pages = {100--100}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2007/11/100}, + doi = {10/c7xmmn}, abstract = {We discuss two inequivalent ways for describing magnetized D-branes wrapped N times on a torus T\^2. The first one is based on a non-abelian gauge bundle U(N), while the second one is obtained by means of a Narain T-duality transformation acting on a theory with non-magnetized branes. We construct in both descriptions the boundary state and the open string vertices and show that they give rise to different string amplitudes. In particular, the description based on the gauge bundle has open string vertex operators with momentum dependent Chan-Paton factors.}, - annotation = {ZSCC: 0000022}, archivePrefix = {arXiv}, eprint = {0709.4149}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/di_vecchia_et_al_2007_wrapped_magnetized_branes.pdf}, - issue = {11}, - number = {DSF-32-2007, NORDITA-2007-28}, - primaryClass = {hep-th} + number = {11} } @article{DiVecchia:2011:OpenStringsSystem, @@ -1558,7 +1250,7 @@ volume = {44}, pages = {245401}, issn = {1751-8113, 1751-8121}, - doi = {10.1088/1751-8113/44/24/245401}, + doi = {10/brf7sk}, abstract = {We construct the six-dimensional Lagrangian for the massless twisted open strings with one end-point ending on a stack of D5 and the other on a stack of D9 branes, interacting with the gauge multiplets living respectively on the D5 and D9 branes. It is first obtained by uplifting to six dimensions the four-dimensional Lagrangian of the N=2 hypermultiplet and manifestly exhibits an SU(2) symmetry. We show by an explicit calculation that it is N=1 supersymmetric in six dimensions and then we check various terms of this Lagrangian by computing string amplitudes on the disk. Finally, starting from this Lagrangian and assuming the presence of non-zero magnetic fluxes along the extra compact dimensions, we determine the spectrum of the Kaluza-Klein states which agrees with the corresponding one obtained from string theory in the field theory limit.}, archivePrefix = {arXiv}, eprint = {1101.0120}, @@ -1576,8 +1268,7 @@ volume = {261}, pages = {678--686}, issn = {05503213}, - doi = {10.1016/0550-3213(85)90593-0}, - annotation = {http://web.archive.org/web/20201001140216/https://linkinghub.elsevier.com/retrieve/pii/0550321385905930}, + doi = {10/fnwxts}, keywords = {archived}, langid = {english} } @@ -1591,8 +1282,7 @@ volume = {274}, pages = {285--314}, issn = {05503213}, - doi = {10.1016/0550-3213(86)90287-7}, - annotation = {http://web.archive.org/web/20201001140250/https://linkinghub.elsevier.com/retrieve/pii/0550321386902877}, + doi = {10/bv9nwg}, keywords = {archived}, langid = {english}, number = {2} @@ -1607,7 +1297,7 @@ volume = {2003}, pages = {046--046}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2003/05/046}, + doi = {10/fktbj2}, abstract = {We discuss systematic approaches to the classification of string/M theory vacua, and physical questions this might help us resolve. To this end, we initiate the study of ensembles of effective Lagrangians, which can be used to precisely study the predictive power of string theory, and in simple examples can lead to universality results. Using these ideas, we outline an approach to estimating the number of vacua of string/M theory which can realize the Standard Model.}, archivePrefix = {arXiv}, eprint = {hep-th/0303194}, @@ -1616,43 +1306,6 @@ number = {05} } -@article{Douglas:2004:BasicResultsVacuum, - title = {Basic Results in Vacuum Statistics}, - author = {Douglas, Michael R.}, - date = {2004}, - journaltitle = {Comptes Rendus Physique}, - shortjournal = {Comptes Rendus Physique}, - volume = {5}, - pages = {965--977}, - issn = {16310705}, - doi = {10.1016/j.crhy.2004.09.008}, - archivePrefix = {arXiv}, - eprint = {hep-th/0409207}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/douglas_2004_basic_results_in_vacuum_statistics2.pdf}, - keywords = {archived}, - langid = {english}, - number = {9-10} -} - -@article{Douglas:2007:FluxCompactification, - title = {Flux Compactification}, - author = {Douglas, Michael R. and Kachru, Shamit}, - date = {2007}, - journaltitle = {Reviews of Modern Physics}, - shortjournal = {Rev. Mod. Phys.}, - volume = {79}, - pages = {733--796}, - issn = {0034-6861, 1539-0756}, - doi = {10.1103/RevModPhys.79.733}, - archivePrefix = {arXiv}, - eprint = {hep-th/0610102}, - eprinttype = {arxiv}, - keywords = {archived}, - langid = {english}, - number = {2} -} - @article{Douglas:2007:LandscapeIntersectingBrane, title = {The Landscape of Intersecting Brane Models}, author = {Douglas, Michael R. and Taylor, Washington}, @@ -1662,7 +1315,7 @@ volume = {2007}, pages = {031--031}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2007/01/031}, + doi = {10/dm8rxf}, archivePrefix = {arXiv}, eprint = {hep-th/0606109}, eprinttype = {arxiv}, @@ -1672,7 +1325,6 @@ } @inproceedings{Drucker:1997:SupportVectorRegression, - ids = {Drucker:1996:SupportVectorRegression}, title = {Support Vector Regression Machines}, booktitle = {Advances in Neural Information Processing Systems}, author = {Drucker, Harris and Burges, Christopher JC and Kaufman, Linda and Smola, Alex J and Vapnik, Vladimir}, @@ -1691,7 +1343,7 @@ volume = {2007}, pages = {042--042}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2007/12/042}, + doi = {10/dptb7d}, abstract = {We consider toroidal compactifications of bosonic string theory with particular regard to the phases (cocycles) necessary for a consistent definition of the vertex operators, the boundary states and the T-duality rules. We use these ingredients to compute the planar multi-loop partition function describing the interaction among magnetized or intersecting D-branes, also in presence of open string moduli. It turns out that unitarity in the open string channel crucially depends on the presence of the cocycles. We then focus on the 2-loop case and study the degeneration limit where this partition function is directly related to the tree-level 3-point correlators between twist fields. These correlators represent the main ingredient in the computation of Yukawa couplings and other terms in the effective action for D-brane phenomenological models. By factorizing the 2-loop partition function we are able to compute the 3-point couplings for abelian twist fields on generic non-factorized tori, thus generalizing previous expressions valid for the 2-torus.}, archivePrefix = {arXiv}, eprint = {0709.1805}, @@ -1700,34 +1352,6 @@ number = {12} } -@article{Engberg:1993:AlgorithmComputingFourRamond, - title = {An Algorithm for Computing Four-{{Ramond}} Vertices at Arbitrary Level}, - author = {Engberg, Niclas and Nilsson, Bengt E.W. and Sundell, Per}, - date = {1993}, - journaltitle = {Nuclear Physics B}, - shortjournal = {Nuclear Physics B}, - volume = {404}, - pages = {187--214}, - issn = {05503213}, - doi = {10.1016/0550-3213(93)90478-8}, - file = {/home/riccardo/.local/share/zotero/files/engberg_et_al_1993_an_algorithm_for_computing_four-ramond_vertices_at_arbitrary_level.pdf}, - keywords = {archived}, - langid = {english}, - number = {1-2} -} - -@online{Erbin:2018:GANsGeneratingEFT, - title = {{{GANs}} for Generating {{EFT}} Models}, - author = {Erbin, Harold and Krippendorf, Sven}, - date = {2018}, - abstract = {We initiate a way of generating models by the computer, satisfying both experimental and theoretical constraints. In particular, we present a framework which allows the generation of effective field theories. We use Generative Adversarial Networks to generate these models and we generate examples which go beyond the examples known to the machine. As a starting point, we apply this idea to the generation of supersymmetric field theories. In this case, the machine knows consistent examples of supersymmetric field theories with a single field and generates new examples of such theories. In the generated potentials we find distinct properties, here the number of minima in the scalar potential, with values not found in the training data. We comment on potential further applications of this framework.}, - archivePrefix = {arXiv}, - eprint = {1809.02612}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/erbin_krippendorf_2018_gans_for_generating_eft_models2.pdf;/home/riccardo/.local/share/zotero/storage/RPXMP3QD/1809.html}, - keywords = {⛔ No DOI found} -} - @online{Erbin:2020:InceptionNeuralNetwork, title = {Inception {{Neural Network}} for {{Complete Intersection Calabi}}-{{Yau}} 3-Folds}, author = {Erbin, Harold and Finotello, Riccardo}, @@ -1753,41 +1377,6 @@ keywords = {⛔ No DOI found} } -@article{Erler:1993:HigherTwistedSector, - title = {Higher {{Twisted Sector Couplings}} of {{Z}}{{{\textsubscript{N}}}} {{Orbifolds}}}, - author = {Erler, Jens and Jungnickel, Dirk-U. and Spaliński, Michał and Stieberger, Stephan}, - date = {1993}, - journaltitle = {Nuclear Physics B}, - shortjournal = {Nuclear Physics B}, - volume = {397}, - pages = {379--414}, - issn = {05503213}, - doi = {10.1016/0550-3213(93)90348-S}, - abstract = {We derive the basic correlation functions of twist fields coming from arbitrary twisted sectors in symmetric \$Z\_N\$ orbifold conformal field theories, keeping all the admissible marginal perturbations, in particular those corresponding to the antisymmetric tensor background field. This allows a thorough investigation of modular symmetries in this type of string compactification. Such a study is explicitly carried out for the group generated by duality transformations. Thus, apart from being of phenomenological use, our couplings are also interesting from the mathematical point of view as they represent automorphic functions for a large class of discrete groups.}, - archivePrefix = {arXiv}, - eprint = {hep-th/9207049}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/erler_et_al_1993_higher_twisted_sector_couplings_of_$z_n$_orbifolds.pdf}, - number = {1-2} -} - -@article{Estrada:2012:GeneralIntegral, - title = {A {{General Integral}}}, - author = {Estrada, Ricardo and Vindas, Jasson}, - date = {2012}, - journaltitle = {Dissertationes Mathematicae}, - shortjournal = {Dissertationes Math.}, - volume = {483}, - pages = {1--49}, - issn = {0012-3862, 1730-6310}, - doi = {10.4064/dm483-0-1}, - abstract = {We define an integral, the distributional integral of functions of one real variable, that is more general than the Lebesgue and the Denjoy-Perron-Henstock-Kurzweil integrals, and which allows the integration of functions with distributional values everywhere or nearly everywhere. Our integral has the property that if \$f\$ is locally distributionally integrable over the real line and \$\textbackslash psi\textbackslash in\textbackslash mathcal\{D\}(\textbackslash mathbb\{R\}\%) \$ is a test function, then \$f\textbackslash psi\$ is distributionally integrable, and the formula\% [{$<\backslash$}mathsf\{f\},\textbackslash psi{$>$} =(\textbackslash mathfrak\{dist\}) \textbackslash int\_\{-\textbackslash infty\}\^\{\textbackslash infty\}f(x) \textbackslash psi(x) \textbackslash,\textbackslash mathrm\{d\}\% x\textbackslash,,] defines a distribution \$\textbackslash mathsf\{f\}\textbackslash in\textbackslash mathcal\{D\}\^\{\textbackslash prime\}(\textbackslash mathbb\{R\}) \$ that has distributional point values almost everywhere and actually \$\textbackslash mathsf\{f\}(x) =f(x) \$ almost everywhere. The indefinite distributional integral \$F(x) =(\textbackslash mathfrak\{dist\}) \textbackslash int\_\{a\}\^\{x\}f(t) \textbackslash,\textbackslash mathrm\{d\}t\$ corresponds to a distribution with point values everywhere and whose distributional derivative has point values almost everywhere equal to \$f(x).\$ The distributional integral is more general than the standard integrals, but it still has many of the useful properties of those standard ones, including integration by parts formulas, substitution formulas, even for infinite intervals --in the Ces\textbackslash `\{a\}ro sense--, mean value theorems, and convergence theorems. The distributional integral satisfies a version of Hake's theorem. Unlike general distributions, locally distributionally integrable functions can be restricted to closed sets and can be multiplied by power functions with real positive exponents.}, - archivePrefix = {arXiv}, - eprint = {1109.2958}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/estrada_vindas_2012_a_general_integral.pdf;/home/riccardo/.local/share/zotero/storage/34MFYX8V/1109.html} -} - @article{Faraggi:2020:MachineLearningClassification, title = {Towards Machine Learning in the Classification of {{Z}}{\textsubscript{2}} × {{Z}}{\textsubscript{2}} Orbifold Compactifications}, author = {Faraggi, A E and Harries, G and Percival, B and Rizos, J}, @@ -1797,7 +1386,7 @@ volume = {1586}, pages = {012032}, issn = {1742-6588, 1742-6596}, - doi = {10.1088/1742-6596/1586/1/012032}, + doi = {10/ghf4nz}, archivePrefix = {arXiv}, eprint = {1901.04448}, eprinttype = {arxiv}, @@ -1811,21 +1400,18 @@ author = {Fawcett, Tom}, date = {2001}, pages = {131--138}, - doi = {10.1109/ICDM.2001.989510}, + doi = {10/d7q2hk}, file = {/home/riccardo/.local/share/zotero/files/fawcett_2001_using_rule_sets_to_maximize_roc_performance2.pdf} } @article{Fernandez-Delgado:2014:WeNeedHundreds, - ids = {Fernandez-Delgado:2014:WeNeedHundredsa}, title = {Do We {{Need Hundreds}} of {{Classifiers}} to {{Solve Real World Classification Problems}}?}, author = {Fernández-Delgado, Manuel and Cernadas, Eva and Barro, Senén and Amorim, Dinani}, date = {2014}, journaltitle = {Journal of Machine Learning Research}, volume = {15}, pages = {3133--3181}, - publisher = {{JMLR. org}}, url = {http://jmlr.org/papers/v15/delgado14a.html}, - urldate = {2020-05-23}, abstract = {We evaluate 179 classifiers arising from 17 families (discriminant analysis, Bayesian, neural networks, support vector machines, decision trees, rule-based classifiers, boosting, bagging, stacking, random forests and other ensembles, generalized linear models, nearest-neighbors, partial least squares and principal component regression, logistic and multinomial regression, multiple adaptive regression splines and other methods), implemented in Weka, R (with and without the caret package), C and Matlab, including all the relevant classifiers available today. We use 121 data sets, which represent the whole UCI data base (excluding the large- scale problems) and other own real problems, in order to achieve significant conclusions about the classifier behavior, not dependent on the data set collection. The classifiers most likely to be the bests are the random forest (RF) versions, the best of which (implemented in R and accessed via caret) achieves 94.1\% of the maximum accuracy overcoming 90\% in the 84.3\% of the data sets. However, the difference is not statistically significant with the second best, the SVM with Gaussian kernel implemented in C using LibSVM, which achieves 92.3\% of the maximum accuracy. A few models are clearly better than the remaining ones: random forest, SVM with Gaussian and polynomial kernels, extreme learning machine with Gaussian kernel, C5.0 and avNNet (a committee of multi-layer perceptrons implemented in R with the caret package). The random forest is clearly the best family of classifiers (3 out of 5 bests classifiers are RF), followed by SVM (4 classifiers in the top-10), neural networks and boosting ensembles (5 and 3 members in the top-20, respectively).}, file = {/home/riccardo/.local/share/zotero/files/fernández-delgado_et_al_2014_do_we_need_hundreds_of_classifiers_to_solve_real_world_classification_problems.pdf}, keywords = {⛔ No DOI found}, @@ -1841,7 +1427,7 @@ volume = {2001}, pages = {011--011}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2001/12/011}, + doi = {10/c2bshm}, abstract = {We classify generalised supersymmetric fluxbranes in type II string theory obtained as Kaluza-Klein reductions of the Minkowski space vacuum of eleven-dimensional supergravity. We obtain two families of smooth solutions which contains all the known solutions, new solutions called nullbranes, and solutions interpolating between them. We explicitly construct all the solutions and we study the U-duality orbits of some of these backgrounds.}, archivePrefix = {arXiv}, eprint = {hep-th/0110170}, @@ -1871,7 +1457,7 @@ volume = {941}, pages = {158--194}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2019.02.010}, + doi = {10/gf66b3}, abstract = {We consider the classical instantonic contribution to the open string configuration associated with three D-branes with relative rotation matrices in SO(4) which corresponds to the computation of the classical part of the correlator of three non Abelian twist fields. We write the classical solution as a sum of a product of two hypergeometric functions. Differently from all the previous cases with three D-branes, the solution is not holomorphic and suggests that the classical bosonic string knows when the configuration may be supersymmetric. We show how this configuration reduces to the standard Abelian twist field computation. From the phenomenological point of view, the Yukawa couplings between chiral matter at the intersection in this configuration are more suppressed with respect to the factorized case in the literature.}, archivePrefix = {arXiv}, eprint = {1812.04643}, @@ -1888,7 +1474,7 @@ volume = {2018}, pages = {169}, issn = {1029-8479}, - doi = {10.1007/JHEP08(2018)169}, + doi = {10/gf66b4}, abstract = {We compute Yukawa couplings in type IIB string theory compactified on a non factorisable six-torus in the presence of D9 branes and fluxes. The setting studied in detail, is obtained by T-dualising an intersecting brane configuration of type IIA theory compactified on a torus generated by the SO(12) root lattice. Particular deformations of such torus are taken into account and provide moduli dependent couplings. Agreement with the type IIA result is found in a non trivial way. The classical type IIB calculation gives also information on a factor accessible only by quantum computations on the type IIA side.}, archivePrefix = {arXiv}, eprint = {1802.05136}, @@ -1897,24 +1483,6 @@ number = {8} } -@article{Frampton:2001:ClassificationConformalityModels, - title = {Classification of {{Conformality Models Based}} on {{Nonabelian Orbifolds}}}, - author = {Frampton, Paul H. and Kephart, Thomas W.}, - date = {2001}, - journaltitle = {Physical Review D}, - shortjournal = {Phys. Rev. D}, - volume = {64}, - pages = {086007}, - issn = {0556-2821, 1089-4918}, - doi = {10.1103/PhysRevD.64.086007}, - abstract = {A systematic analysis is presented of compactifications of the IIB superstring on \$AdS\_5 \textbackslash times S\^5/\textbackslash Gamma\$ where \$\textbackslash Gamma\$ is a non-abelian discrete group. Every possible \$\textbackslash Gamma\$ with order \$g \textbackslash leq 31\$ is considered. There exist 45 such groups but a majority cannot yield chiral fermions due to a certain theorem that is proved. The lowest order to embrace the nonSUSY standard \$SU(3) \textbackslash times SU(2) \textbackslash times U(1)\$ model with three chiral families is \$\textbackslash Gamma = D\_4 \textbackslash times Z\_3\$, with \$g=24\$; this is the only successful model found in the search. The consequent uniqueness of the successful model arises primarily from the scalar sector, prescribed by the construction, being sufficient to allow the correct symmetry breakdown.}, - archivePrefix = {arXiv}, - eprint = {hep-th/0011186}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/frampton_kephart_2001_classification_of_conformality_models_based_on_nonabelian_orbifolds5.pdf}, - number = {8} -} - @article{Friedan:1986:ConformalInvarianceSupersymmetry, title = {Conformal Invariance, Supersymmetry and String Theory}, author = {Friedan, Daniel and Martinec, Emil and Shenker, Stephen}, @@ -1923,14 +1491,13 @@ volume = {271}, pages = {93--165}, issn = {05503213}, - doi = {10.1016/s0550-3213(86)80006-2}, + doi = {10/fq6qtz}, abstract = {Covariant quantization of string theories is developed in the context of conformal field theory and the BRST quantization procedure. The BRST method is used to covariantly quantize superstrings, and in particular to construct the vertex operators for string emission as well as the supersymmetry charge. The calculation of string loop diagrams is sketched. We discuss how conformal methods can be used to study string compactification and dynamics. © 1986, Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division). All rights reserved. All rights reserved.}, file = {/home/riccardo/.local/share/zotero/files/friedan_et_al_1986_conformal_invariance,_supersymmetry_and_string_theory.pdf}, number = {3-4} } @article{Friedman:2001:GreedyFunctionApproximation, - ids = {Friedman:2001:GreedyFunctionApproximationa}, title = {Greedy {{Function Approximation}}: {{A Gradient Boosting Machine}}}, shorttitle = {Greedy {{Function Approximation}}}, author = {Friedman, Jerome H.}, @@ -1938,14 +1505,12 @@ journaltitle = {The Annals of Statistics}, volume = {29}, pages = {1189--1232}, - publisher = {{Institute of Mathematical Statistics}}, issn = {0090-5364}, - doi = {10.1214/aos/1013203451}, + doi = {10/fbgj35}, abstract = {Function estimation/approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest-descent minimization. A general gradient descent "boosting" paradigm is developed for additive expansions based on any fitting criterion. Specific algorithms are presented for least-squares, least absolute deviation, and Huber-M loss functions for regression, and multiclass logistic likelihood for classification. Special enhancements are derived for the particular case where the individual additive components are regression trees, and tools for interpreting such "TreeBoost" models are presented. Gradient boosting of regression trees produces competitive, highly robust, interpretable procedures for both regression and classification, especially appropriate for mining less than clean data. Connections between this approach and the boosting methods of Freund and Shapire and Friedman, Hastie and Tibshirani are discussed.}, eprint = {2699986}, eprinttype = {jstor}, file = {/home/riccardo/.local/share/zotero/files/friedman_2001_greedy_function_approximation.pdf}, - keywords = {❓ Multiple DOI}, number = {5} } @@ -1957,33 +1522,13 @@ volume = {38}, pages = {367--378}, issn = {0167-9473}, - doi = {10.1016/s0167-9473(01)00065-2}, + doi = {10/fxb956}, file = {/home/riccardo/.local/share/zotero/files/friedman_2002_stochastic_gradient_boosting.pdf;/home/riccardo/.local/share/zotero/storage/RTS7DDDJ/S0167947301000652.html}, number = {4} } -@article{Gan:2017:HolographyDeepLearning, - title = {Holography as Deep Learning}, - author = {Gan, Wen-Cong and Shu, Fu-Wen}, - date = {2017}, - journaltitle = {International Journal of Modern Physics D}, - shortjournal = {Int. J. Mod. Phys. D}, - volume = {26}, - pages = {1743020}, - issn = {0218-2718, 1793-6594}, - doi = {10.1142/S0218271817430209}, - abstract = {Quantum many-body problem with exponentially large degrees of freedom can be reduced to a tractable computational form by neural network method [G. Carleo and M. Troyer, Science 355 (2017) 602, arXiv:1606.02318.] The power of deep neural network (DNN) based on deep learning is clarified by mapping it to renormalization group (RG), which may shed lights on holographic principle by identifying a sequence of RG transformations to the AdS geometry. In this paper, we show that any network which reflects RG process has intrinsic hyperbolic geometry, and discuss the structure of entanglement encoded in the graph of DNN. We find the entanglement structure of DNN is of Ryu–Takayanagi form. Based on these facts, we argue that the emergence of holographic gravitational theory is related to deep learning process of the quantum-field theory.}, - archivePrefix = {arXiv}, - eprint = {1705.05750}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/gan_shu_2017_holography_as_deep_learning2.pdf}, - keywords = {archived}, - langid = {english}, - number = {12} -} - -@article{Gato:1990:VertexOperatorsNonabelian, - title = {Vertex Operators, Non-Abelian Orbifolds and the {{Reimann}}-{{Hilbert}} Problem}, +@article{Gato:1990:VertexOperatorsNonAbelian, + title = {Vertex Operators, Non-{{Abelian}} Orbifolds and the {{Reimann}}--{{Hilbert}} Problem}, author = {Gato, Beatriz}, date = {1990}, journaltitle = {Nuclear Physics B}, @@ -1991,8 +1536,7 @@ volume = {334}, pages = {414--430}, issn = {05503213}, - doi = {10.1016/0550-3213(90)90485-V}, - annotation = {http://web.archive.org/web/20200909163742/https://linkinghub.elsevier.com/retrieve/pii/055032139090485V}, + doi = {10/chx7rp}, file = {/home/riccardo/.local/share/zotero/files/gato_1990_vertex_operators,_non-abelian_orbifolds_and_the_reimann-hilbert_problem.pdf}, keywords = {archived}, langid = {english}, @@ -2008,7 +1552,7 @@ volume = {504}, pages = {214--238}, issn = {05503213}, - doi = {10.1016/S0550-3213(97)00508-7}, + doi = {10/djsprb}, abstract = {We study bound states of D-p-branes and D-(p+2)-branes. By switching on a large magnetic field F on the (p+2) brane, the problem is shown to admit a perturbative analysis in an expansion in inverse powers of F. It is found that, to the leading order in 1/F, the quartic potential of the tachyonic state from the open string stretched between the p- and (p+2)-brane gives a vacuum energy which agrees with the prediction of the BPS mass formula for the bound state. We generalize the discussion to the case of m p-branes plus 1 (p+2)-brane with magnetic field. The T dual picture of this, namely several (p+2)-branes carrying some p-brane charges through magnetic flux is also discussed, where the perturbative treatment is available in the small F limit. We show that once again, in the same approximation, the tachyon condensates give rise to the correct BPS mass formula. The role of 't Hooft's toron configurations in the extension of the above results beyond the quartic approximation as well as the issue of the unbroken gauge symmetries are discussed. We comment on the connection between the present bound state problem and Kondo-like problems in the context of relevant boundary perturbations of boundary conformal field theories.}, archivePrefix = {arXiv}, eprint = {hep-th/9704006}, @@ -2022,26 +1566,12 @@ author = {Géron, Aurélien}, date = {2019}, url = {http://shop.oreilly.com/product/0636920142874.do}, - urldate = {2019-11-06}, abstract = {Through a series of recent breakthroughs, deep learning has boosted the entire field of machine learning. Now, even programmers who know close to nothing about this technology can use simple, efficie...}, - annotation = {http://web.archive.org/web/20200531204023/http://shop.oreilly.com/product/0636920142874.do}, file = {/home/riccardo/.local/share/zotero/files/géron_2019_hands-on_machine_learning_with_scikit-learn,_keras,_and_tensorflow.pdf}, isbn = {978-1-4920-3264-9}, langid = {english} } -@online{Ginsparg:1988:AppliedConformalField, - title = {Applied {{Conformal Field Theory}}}, - author = {Ginsparg, Paul}, - date = {1988}, - abstract = {These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in 2 dimensions 3. The central charge and the Virasoro algebra 4. Kac determinant and unitarity 5. Identication of m = 3 with the critical Ising model 6. Free bosons and fermions 7. Free fermions on a torus 8. Free bosons on a torus 9. Affine Kac-Moody algebras and coset constructions 10. Advanced applications}, - archivePrefix = {arXiv}, - eprint = {hep-th/9108028}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/ginsparg_1988_applied_conformal_field_theory.pdf}, - keywords = {⛔ No DOI found} -} - @inproceedings{Glorot:2011:DeepSparseRectifier, title = {Deep Sparse Rectifier Neural Networks}, booktitle = {Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics}, @@ -2052,25 +1582,6 @@ keywords = {⛔ No DOI found} } -@article{Gmeiner:2006:OneBillionMSSMlike, - title = {One in a Billion: {{MSSM}}-like {{D}}-Brane Statistics}, - shorttitle = {One in a Billion}, - author = {Gmeiner, Florian and Blumenhagen, Ralph and Honecker, Gabriele and Lüst, Dieter and Weigand, Timo}, - date = {2006}, - journaltitle = {Journal of High Energy Physics}, - shortjournal = {J. High Energy Phys.}, - volume = {2006}, - pages = {004--004}, - issn = {1029-8479}, - doi = {10.1088/1126-6708/2006/01/004}, - archivePrefix = {arXiv}, - eprint = {hep-th/0510170}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/gmeiner_et_al_2006_one_in_a_billion.pdf}, - keywords = {archived}, - number = {01} -} - @article{Goddard:1973:QuantumDynamicsMassless, title = {Quantum Dynamics of a Massless Relativistic String}, author = {Goddard, Peter and Goldstone, Jeffrey and Rebbi, Claudio and Thorn, Charles B.}, @@ -2080,7 +1591,7 @@ volume = {56}, pages = {109--135}, issn = {05503213}, - doi = {10.1016/0550-3213(73)90223-X}, + doi = {10/ccmwgf}, file = {/home/riccardo/.local/share/zotero/files/goddard_et_al_1973_quantum_dynamics_of_a_massless_relativistic_string.pdf}, keywords = {archived}, langid = {english}, @@ -2099,6 +1610,17 @@ file = {/home/riccardo/.local/share/zotero/files/goodfellow_et_al_2014_generative_adversarial_nets.pdf} } +@book{Goodfellow:2017:DeepLearning, + title = {Deep Learning}, + author = {Goodfellow, Ian and Yousha, Bengio and Courville, Aaron}, + date = {2017}, + volume = {1}, + publisher = {{MIT press}}, + url = {https://www.deeplearningbook.org/}, + file = {/home/riccardo/.local/share/zotero/files/bengio_et_al_2017_deep_learning.pdf}, + isbn = {978-0-262-33737-3} +} + @inproceedings{Gori:2005:NewModelLearning, title = {A New Model for Learning in Graph Domains}, booktitle = {Proceedings. 2005 {{IEEE}} International Joint Conference on Neural Networks, 2005.}, @@ -2106,13 +1628,11 @@ date = {2005}, volume = {2}, pages = {729--734}, - doi = {10.1109/IJCNN.2005.1555942}, - file = {/home/riccardo/.local/share/zotero/files/gori_et_al_2005_a_new_model_for_learning_in_graph_domains2.pdf}, - organization = {{IEEE}} + doi = {10/cr2f33}, + file = {/home/riccardo/.local/share/zotero/files/gori_et_al_2005_a_new_model_for_learning_in_graph_domains2.pdf} } @article{Grana:2006:FluxCompactificationsString, - ids = {Grana:2005:FluxCompactificationsString}, title = {Flux Compactifications in String Theory: {{A}} Comprehensive Review}, shorttitle = {Flux Compactifications in String Theory}, author = {Graña, Mariana}, @@ -2122,8 +1642,10 @@ volume = {423}, pages = {91--158}, issn = {03701573}, - doi = {10.1016/j.physrep.2005.10.008}, - annotation = {http://web.archive.org/web/20201007105121/https://linkinghub.elsevier.com/retrieve/pii/S0370157305004618}, + doi = {10/bdzzsc}, + archivePrefix = {arXiv}, + eprint = {hep-th/0509003}, + eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/graña_2005_flux_compactifications_in_string_theory.pdf;/home/riccardo/.local/share/zotero/files/graña_2006_flux_compactifications_in_string_theory2.pdf}, keywords = {archived}, langid = {english}, @@ -2134,11 +1656,11 @@ title = {String {{Theory Compactifications}}}, author = {Graña, Mariana and Triendl, Hagen}, date = {2017}, - publisher = {{Springer International Publishing}}, + publisher = {{Springer}}, location = {{Cham}}, - doi = {10.1007/978-3-319-54316-1}, + url = {http://link.springer.com/10.1007/978-3-319-54316-1}, file = {/home/riccardo/.local/share/zotero/files/graña_triendl_2017_string_theory_compactifications.pdf}, - isbn = {978-3-319-54315-4 978-3-319-54316-1}, + isbn = {978-3-319-54315-4}, langid = {english}, series = {{{SpringerBriefs}} in {{Physics}}} } @@ -2152,7 +1674,7 @@ volume = {2013}, pages = {70}, issn = {1029-8479}, - doi = {10.1007/JHEP07(2013)070}, + doi = {10/ghf4n2}, abstract = {We present an exhaustive, constructive, classification of the Calabi-Yau four-folds which can be described as complete intersections in products of projective spaces. A comprehensive list of 921,497 configuration matrices which represent all topologically distinct types of complete intersection Calabi-Yau four-folds is provided and can be downloaded at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html . The manifolds have non-negative Euler characteristics in the range 0 - 2610. This data set will be of use in a wide range of physical and mathematical applications. Nearly all of these four-folds are elliptically fibered and are thus of interest for F-theory model building.}, archivePrefix = {arXiv}, eprint = {1303.1832}, @@ -2170,7 +1692,7 @@ volume = {2014}, pages = {93}, issn = {1029-8479}, - doi = {10.1007/JHEP09(2014)093}, + doi = {10/ghf4n3}, abstract = {We investigate the mathematical properties of the class of Calabi-Yau four-folds recently found in [arXiv:1303.1832]. This class consists of 921,497 configuration matrices which correspond to manifolds that are described as complete intersections in products of projective spaces. For each manifold in the list, we compute the full Hodge diamond as well as additional topological invariants such as Chern classes and intersection numbers. Using this data, we conclude that there are at least 36,779 topologically distinct manifolds in our list. We also study the fibration structure of these manifolds and find that 99.95 percent can be described as elliptic fibrations. In total, we find 50,114,908 elliptic fibrations, demonstrating the multitude of ways in which many manifolds are fibered. A sub-class of 26,088,498 fibrations satisfy necessary conditions for admitting sections. The complete data set can be downloaded at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html .}, archivePrefix = {arXiv}, eprint = {1405.2073}, @@ -2188,7 +1710,7 @@ volume = {109}, pages = {99--108}, issn = {0010-3616, 1432-0916}, - doi = {10.1007/BF01205673}, + doi = {10/bb29bx}, langid = {english}, number = {1} } @@ -2202,7 +1724,7 @@ volume = {113}, pages = {505--528}, issn = {0010-3616, 1432-0916}, - doi = {10.1007/BF01221257}, + doi = {10/fjxkft}, langid = {english}, number = {3} } @@ -2212,7 +1734,6 @@ author = {Green, Michael B. and Schwarz, John H. and Witten, Edward}, date = {1988}, volume = {1}, - doi = {10.1017/CBO9781139248563}, file = {/home/riccardo/.local/share/zotero/files/green_et_al_1988_superstring_theory.pdf}, isbn = {978-0-521-35752-4}, series = {Cambridge Monographs on Mathematical Physics} @@ -2223,7 +1744,6 @@ author = {Green, Michael B. and Schwarz, John H. and Witten, Edward}, date = {1988}, volume = {2}, - doi = {10.1017/CBO9781139248570}, file = {/home/riccardo/.local/share/zotero/files/green_et_al_1988_superstring_theory2.pdf}, isbn = {978-0-521-35753-1}, series = {Cambridge Monographs on Mathematical Physics} @@ -2238,7 +1758,7 @@ volume = {6}, pages = {105--124}, issn = {0264-9381, 1361-6382}, - doi = {10.1088/0264-9381/6/2/006}, + doi = {10/c6d47n}, file = {/home/riccardo/.local/share/zotero/files/green_et_al_1989_all_the_hodge_numbers_for_all_calabi-yau_complete_intersections3.pdf}, keywords = {archived}, number = {2} @@ -2248,8 +1768,6 @@ title = {String {{Theory}} on {{Calabi}}-{{Yau Manifolds}}}, author = {Greene, Brian}, date = {1997}, - url = {http://arxiv.org/abs/hep-th/9702155}, - urldate = {2020-09-03}, abstract = {These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments discussed include new geometric features of string theory which occur even at the classical level as well as those which require non-perturbative effects. These lecture notes are based on an evolving set of lectures presented at a number of schools but most closely follow a series of seven lectures given at the TASI-96 summer school on Strings, Fields and Duality.}, archivePrefix = {arXiv}, eprint = {hep-th/9702155}, @@ -2258,60 +1776,6 @@ keywords = {⛔ No DOI found} } -@article{Grimm:2005:EffectiveActionType, - title = {The Effective Action of Type {{IIA Calabi}}–{{Yau}} Orientifolds}, - author = {Grimm, Thomas W. and Louis, Jan}, - date = {2005}, - journaltitle = {Nuclear Physics B}, - shortjournal = {Nuclear Physics B}, - volume = {718}, - pages = {153--202}, - issn = {05503213}, - doi = {10.1016/j.nuclphysb.2005.04.007}, - annotation = {http://web.archive.org/web/20200905150924/https://linkinghub.elsevier.com/retrieve/pii/S0550321305002920}, - file = {/home/riccardo/.local/share/zotero/files/grimm_louis_2005_the_effective_action_of_type_iia_calabi–yau_orientifolds.pdf}, - keywords = {archived}, - langid = {english}, - number = {1-2} -} - -@article{Halverson:2017:AlgorithmicUniversalityFtheory, - title = {Algorithmic Universality in {{F}}-Theory Compactifications}, - author = {Halverson, James and Long, Cody and Sung, Benjamin}, - date = {2017}, - journaltitle = {Physical Review D}, - shortjournal = {Phys. Rev. D}, - volume = {96}, - pages = {126006}, - issn = {2470-0010, 2470-0029}, - doi = {10.1103/PhysRevD.96.126006}, - archivePrefix = {arXiv}, - eprint = {1706.02299}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/halverson_et_al_2017_algorithmic_universality_in_f-theory_compactifications.pdf}, - keywords = {archived}, - langid = {english}, - number = {12} -} - -@inproceedings{Halverson:2018:TASILecturesRemnants, - title = {{{TASI Lectures}} on {{Remnants}} from the {{String Landscape}}}, - booktitle = {Proceedings of {{Theoretical Advanced Study Institute Summer School}} 2017 "{{Physics}} at the {{Fundamental Frontier}}" — {{PoS}}({{TASI2017}})}, - author = {Halverson, James and Langacker, Paul}, - date = {2018}, - pages = {019}, - publisher = {{Sissa Medialab}}, - location = {{Boulder, Colorado}}, - doi = {10.22323/1.305.0019}, - archivePrefix = {arXiv}, - eprint = {1801.03503}, - eprinttype = {arxiv}, - eventtitle = {Theoretical {{Advanced Study Institute Summer School}} 2017 "{{Physics}} at the {{Fundamental Frontier}}"}, - file = {/home/riccardo/.local/share/zotero/files/halverson_langacker_2018_tasi_lectures_on_remnants_from_the_string_landscape2.pdf}, - keywords = {archived}, - langid = {english} -} - @article{Halverson:2019:BranesBrainsExploring, title = {Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning}, shorttitle = {Branes with Brains}, @@ -2322,7 +1786,7 @@ volume = {2019}, pages = {3}, issn = {1029-8479}, - doi = {10.1007/JHEP06(2019)003}, + doi = {10/gg66j8}, archivePrefix = {arXiv}, eprint = {1903.11616}, eprinttype = {arxiv}, @@ -2340,7 +1804,7 @@ volume = {99}, pages = {046015}, issn = {2470-0010, 2470-0029}, - doi = {10.1103/PhysRevD.99.046015}, + doi = {10/gg66j7}, archivePrefix = {arXiv}, eprint = {1809.08279}, eprinttype = {arxiv}, @@ -2359,7 +1823,7 @@ volume = {68}, pages = {2000005}, issn = {0015-8208, 1521-3978}, - doi = {10.1002/prop.202000005}, + doi = {10/gg66j9}, archivePrefix = {arXiv}, eprint = {2001.00555}, eprinttype = {arxiv}, @@ -2378,7 +1842,7 @@ volume = {2003}, pages = {034--034}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2003/06/034}, + doi = {10/fd2kjv}, abstract = {We provide a simple low energy description of recombination of intersecting D-branes using super Yang-Mills theory. The recombination is realized by condensation of an off-diagonal tachyonic fluctuation localized at the intersecting point. The recombination process is equivalent to brane-antibrane annihilation, thus our result confirms Sen's conjecture on tachyon condensation, although we work in the super Yang-Mills theory whose energy scale is much lower than alpha'. We also discuss the decay width of non-parallelly separated D-branes.}, archivePrefix = {arXiv}, eprint = {hep-th/0303204}, @@ -2387,64 +1851,6 @@ number = {06} } -@article{Hashimoto:2018:DeepLearningAdS, - title = {Deep Learning and the {{AdS}} / {{CFT}} Correspondence}, - author = {Hashimoto, Koji and Sugishita, Sotaro and Tanaka, Akinori and Tomiya, Akio}, - date = {2018}, - journaltitle = {Physical Review D}, - shortjournal = {Phys. Rev. D}, - volume = {98}, - pages = {046019}, - issn = {2470-0010, 2470-0029}, - doi = {10.1103/PhysRevD.98.046019}, - annotation = {http://web.archive.org/web/20201007124217/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.046019}, - archivePrefix = {arXiv}, - eprint = {1802.08313}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/hashimoto_et_al_2018_deep_learning_and_ads-cft.pdf;/home/riccardo/.local/share/zotero/files/hashimoto_et_al_2018_deep_learning_and_the_ads_-_cft_correspondence.pdf}, - keywords = {archived}, - langid = {english}, - number = {4} -} - -@article{Hashimoto:2018:DeepLearningHolographic, - title = {Deep Learning and Holographic {{QCD}}}, - author = {Hashimoto, Koji and Sugishita, Sotaro and Tanaka, Akinori and Tomiya, Akio}, - date = {2018}, - journaltitle = {Physical Review D}, - shortjournal = {Phys. Rev. D}, - volume = {98}, - pages = {106014}, - issn = {2470-0010, 2470-0029}, - doi = {10.1103/PhysRevD.98.106014}, - archivePrefix = {arXiv}, - eprint = {1809.10536}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/hashimoto_et_al_2018_deep_learning_and_holographic_qcd3.pdf}, - keywords = {archived}, - langid = {english}, - number = {10} -} - -@article{Hashimoto:2019:AdSCFTCorrespondence, - title = {{{AdS}} / {{CFT}} Correspondence as a Deep {{Boltzmann}} Machine}, - author = {Hashimoto, Koji}, - date = {2019}, - journaltitle = {Physical Review D}, - shortjournal = {Phys. Rev. D}, - volume = {99}, - pages = {106017}, - issn = {2470-0010, 2470-0029}, - doi = {10.1103/PhysRevD.99.106017}, - archivePrefix = {arXiv}, - eprint = {1903.04951}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/hashimoto_2019_ads_-_cft_correspondence_as_a_deep_boltzmann_machine.pdf}, - keywords = {archived}, - langid = {english}, - number = {10} -} - @article{He:2017:MachinelearningStringLandscape, title = {Machine-Learning the String Landscape}, author = {He, Yang-Hui}, @@ -2454,60 +1860,29 @@ volume = {774}, pages = {564--568}, issn = {03702693}, - doi = {10.1016/j.physletb.2017.10.024}, + doi = {10/gcqfzv}, file = {/home/riccardo/.local/share/zotero/files/he_2017_machine-learning_the_string_landscape3.pdf}, keywords = {archived}, langid = {english} } -@article{He:2019:DistinguishingEllipticFibrations, - title = {Distinguishing Elliptic Fibrations with {{AI}}}, - author = {He, Yang-Hui and Lee, Seung-Joo}, - date = {2019}, - journaltitle = {Physics Letters B}, - shortjournal = {Physics Letters B}, - volume = {798}, - pages = {134889}, - issn = {03702693}, - doi = {10.1016/j.physletb.2019.134889}, - archivePrefix = {arXiv}, - eprint = {1904.08530}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/he_lee_2019_distinguishing_elliptic_fibrations_with_ai5.pdf}, - keywords = {archived}, - langid = {english} -} - -@online{He:2020:CalabiYauSpacesString, - title = {Calabi-{{Yau Spaces}} in the {{String Landscape}}}, - author = {He, Yang-Hui}, - date = {2020}, - abstract = {Calabi-Yau spaces, or Kahler spaces admitting zero Ricci curvature, have played a pivotal role in theoretical physics and pure mathematics for the last half-century. In physics, they constituted the first and natural solution to compactification of superstring theory to our 4-dimensional universe, primarily due to one of their equivalent definitions being the admittance of covariantly constant spinors. Since the mid-1980s, physicists and mathematicians have joined forces in creating explicit examples of Calabi-Yau spaces, compiling databases of formidable size, including the complete intersecion (CICY) dataset, the weighted hypersurfaces dataset, the elliptic-fibration dataset, the Kreuzer-Skarke toric hypersurface dataset, generalized CICYs etc., totaling at least on the order of 10\^10 manifolds. These all contribute to the vast string landscape, the multitude of possible vacuum solutions to string compactification. More recently, this collaboration has been enriched by computer science and data science, the former, in bench-marking the complexity of the algorithms in computing geometric quantities and the latter, in applying techniques such as machine-learning in extracting unexpected information. These endeavours, inspired by the physics of the string landscape, have rendered the investigation of Calabi-Yau spaces one of the most exciting and inter-disciplinary fields. Invited contribution to the Oxford Research Encyclopedia of Physics, B.\textasciitilde Foster Ed., OUP, 2020}, - archivePrefix = {arXiv}, - eprint = {2006.16623}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/he_2020_calabi-yau_spaces_in_the_string_landscape.pdf}, - keywords = {⛔ No DOI found} -} - @software{Head:2020:ScikitoptimizeScikitoptimize, title = {Scikit-Optimize/Scikit-Optimize}, author = {Head, Tim and Kumar, Manoj and Nahrstaedt, Holger and Louppe, Gilles and Shcherbatyi, Iaroslav}, date = {2020}, - doi = {10.5281/zenodo.4014775}, + url = {https://zenodo.org/record/4014775}, organization = {{Zenodo}}, version = {v0.8.1} } @inproceedings{Ho:1995:RandomDecisionForests, - ids = {TinKamHo:1995:RandomDecisionForests}, title = {Random Decision Forests}, booktitle = {Proceedings of 3rd {{International Conference}} on {{Document Analysis}} and {{Recognition}}}, author = {Ho, Tin Kam}, date = {1995}, volume = {1}, pages = {278-282 vol.1}, - doi = {10.1109/icdar.1995.598994}, + doi = {10/c7x7s8}, abstract = {Decision trees are attractive classifiers due to their high execution speed. But trees derived with traditional methods often cannot be grown to arbitrary complexity for possible loss of generalization accuracy on unseen data. The limitation on complexity usually means suboptimal accuracy on training data. Following the principles of stochastic modeling, we propose a method to construct tree-based classifiers whose capacity can be arbitrarily expanded for increases in accuracy for both training and unseen data. The essence of the method is to build multiple trees in randomly selected subspaces of the feature space. Trees in, different subspaces generalize their classification in complementary ways, and their combined classification can be monotonically improved. The validity of the method is demonstrated through experiments on the recognition of handwritten digits.}, eventtitle = {Proceedings of 3rd {{International Conference}} on {{Document Analysis}} and {{Recognition}}}, file = {/home/riccardo/.local/share/zotero/files/ho_1995_random_decision_forests.pdf;/home/riccardo/.local/share/zotero/storage/I7UUJXK7/598994.html} @@ -2521,7 +1896,7 @@ volume = {60}, pages = {1050--1056}, issn = {00158208}, - doi = {10.1002/prop.201200016}, + doi = {10/fz4mj9}, abstract = {We present the perturbative Yukawa couplings of the Standard Model on fractional intersecting D6-branes on T6/Z6' and discuss two mechanisms of creating mass terms for the vector-like particles in the matter spectrum, through perturbative three-point couplings and through continuous D6-brane displacements.}, archivePrefix = {arXiv}, eprint = {1201.5872}, @@ -2539,8 +1914,7 @@ volume = {258}, pages = {91--96}, issn = {03702693}, - doi = {10.1016/0370-2693(91)91214-G}, - annotation = {http://web.archive.org/web/20201001140650/https://linkinghub.elsevier.com/retrieve/pii/037026939191214G}, + doi = {10/dzbvx3}, keywords = {archived}, langid = {english}, number = {1-2} @@ -2555,8 +1929,10 @@ volume = {66}, pages = {103512}, issn = {0556-2821, 1089-4918}, - doi = {10.1103/PhysRevD.66.103512}, - annotation = {http://web.archive.org/web/20201001150603/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.66.103512}, + doi = {10/frkxrv}, + archivePrefix = {arXiv}, + eprint = {hep-th/0206228}, + eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/horowitz_polchinski_2002_instability_of_spacelike_and_null_orbifold_singularities.pdf}, keywords = {archived}, langid = {english}, @@ -2564,10 +1940,11 @@ } @book{Hubsch:1992:CalabiyauManifoldsBestiary, - title = {Calabi-Yau Manifolds: {{A}} Bestiary for Physicists}, + title = {Calabi-Yau Manifolds: A Bestiary for Physicists}, author = {Hübsch, Tristan}, date = {1992}, publisher = {{World Scientific}}, + url = {https://www.worldscientific.com/worldscibooks/10.1142/1410}, file = {/home/riccardo/.local/share/zotero/files/hubsch_1992_calabi-yau_manifolds.pdf}, isbn = {978-981-02-1927-7} } @@ -2579,7 +1956,7 @@ journaltitle = {Computing in Science Engineering}, volume = {9}, pages = {90--95}, - doi = {10.1109/MCSE.2007.55}, + doi = {10/drbjhg}, number = {3} } @@ -2592,7 +1969,7 @@ volume = {2001}, pages = {002--002}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2001/11/002}, + doi = {10/drzgmv}, archivePrefix = {arXiv}, eprint = {hep-th/0105155}, eprinttype = {arxiv}, @@ -2607,7 +1984,7 @@ date = {2012}, publisher = {{Cambridge University Press}}, file = {/home/riccardo/.local/share/zotero/files/ibanez_uranga_2012_string_theory_and_particle_physics2.pdf}, - isbn = {978-0-521-51752-2 978-1-139-22742-1} + isbn = {978-0-521-51752-2} } @article{Inoue:1987:NonAbelianOrbifolds, @@ -2619,8 +1996,7 @@ volume = {78}, pages = {908--922}, issn = {0033-068X, 1347-4081}, - doi = {10.1143/PTP.78.908}, - annotation = {http://web.archive.org/web/20200909163620/https://academic.oup.com/ptp/article/78/4/908/1865644}, + doi = {10/bfp9q4}, file = {/home/riccardo/.local/share/zotero/files/inoue_et_al_1987_non-abelian_orbifolds2.pdf}, keywords = {archived}, langid = {english}, @@ -2636,7 +2012,7 @@ volume = {84}, pages = {702--727}, issn = {0033-068X, 1347-4081}, - doi = {10.1143/ptp/84.4.702}, + doi = {10/ghf4n4}, file = {/home/riccardo/.local/share/zotero/files/inoue_nima_1990_string_interactions_on_non-abelian_orbifold.pdf}, keywords = {archived}, langid = {english}, @@ -2657,7 +2033,6 @@ } @article{Jackiw:1992:ElectromagneticFieldsMassless, - ids = {Jackiw:1992:ElectromagneticFieldsMasslessa}, title = {Electromagnetic Fields of a Massless Particle and the Eikonal}, author = {Jackiw, R. and Kabat, D. and Ortiz, M.}, date = {1992}, @@ -2666,36 +2041,20 @@ volume = {277}, pages = {148--152}, issn = {0370-2693}, - doi = {10.1016/0370-2693(92)90971-6}, + doi = {10/fs877h}, abstract = {Electromagnetic fields of a massless charged particle are described by a gauge potential that is almost everywhere a pure gauge. Solution of quantum mechanical wave equations in the presence of such fields is therefore immediate and leads to a new derivation of the quantum electrodynamical eikonal approximation. The electromagnetic action in the eikonal limit is localized on a contour in a two-dimensional Minkowski subspace of four-dimensional space-time. The exact S-matrix of this reduced theory reproduces the eikonal approximation. In this way, we apply the recent gravitational consideration of't Hooft as well and Verlinde and Verlinde to electromagnetism.}, - annotation = {ZSCC: 0000091}, archivePrefix = {arXiv}, eprint = {hep-th/9112020}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/jackiw_et_al_1992_electromagnetic_fields_of_a_massless_particle_and_the_eikonal.pdf}, - issue = {1}, - number = {MIT-CTP-2033} -} - -@article{Johnson:2000:DBranePrimer, - title = {D-{{Brane Primer}}}, - author = {Johnson, Clifford V.}, - date = {2000}, - journaltitle = {Strings, Branes and Gravity}, - pages = {129--350}, - doi = {10.1142/9789812799630_0002}, - abstract = {Following is a collection of lecture notes on D-branes, which may be used by the reader as preparation for applications to modern research applications such as: the AdS/CFT and other gauge theory/geometry correspondences, Matrix Theory and stringy non-commutative geometry, etc. In attempting to be reasonably self-contained, the notes start from classical point-particles and develop the subject logically (but selectively) through classical strings, quantisation, D-branes, supergravity, superstrings, string duality, including many detailed applications. Selected focus topics feature D-branes as probes of both spacetime and gauge geometry, highlighting the role of world-volume curvature and gauge couplings, with some non-Abelian cases. Other advanced topics which are discussed are the (presently) novel tools of research such as fractional branes, the enhancon mechanism, D(ielectric)-branes and the emergence of the fuzzy/non-commutative sphere.}, - archivePrefix = {arXiv}, - eprint = {hep-th/0007170}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/johnson_2000_d-brane_primer.pdf} + number = {1} } @book{Joyce:2000:CompactManifoldsSpecial, title = {Compact Manifolds with Special Holonomy}, author = {Joyce, Dominic}, date = {2000}, - publisher = {{Oxford University Press on Demand}}, + publisher = {{Oxford University Press}}, file = {/home/riccardo/.local/share/zotero/files/joyce_2000_compact_manifolds_with_special_holonomy.pdf}, isbn = {978-0-19-850601-0} } @@ -2721,7 +2080,7 @@ volume = {68}, pages = {046005}, issn = {0556-2821, 1089-4918}, - doi = {10.1103/PhysRevD.68.046005}, + doi = {10/bfvjj7}, abstract = {We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of anti-D3 branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is much greater than the cosmological timescale of 10\^10 years. We also prove, under certain conditions, that the lifetime of dS space in string theory will always be shorter than the recurrence time.}, archivePrefix = {arXiv}, eprint = {hep-th/0301240}, @@ -2730,37 +2089,16 @@ number = {4} } -@article{Khoury:2002:BigCrunchBig, - title = {From {{Big Crunch}} to {{Big Bang}}}, - author = {Khoury, Justin and Ovrut, Burt A. and Seiberg, Nathan and Steinhardt, Paul J. and Turok, Neil}, - date = {2002}, - journaltitle = {Physical Review D}, - shortjournal = {Phys. Rev. D}, - volume = {65}, - pages = {086007}, - issn = {0556-2821, 1089-4918}, - doi = {10.1103/PhysRevD.65.086007}, - abstract = {We consider conditions under which a universe contracting towards a big crunch can make a transition to an expanding big bang universe. A promising example is 11-dimensional M-theory in which the eleventh dimension collapses, bounces, and re-expands. At the bounce, the model can reduce to a weakly coupled heterotic string theory and, we conjecture, it may be possible to follow the transition from contraction to expansion. The possibility opens the door to new classes of cosmological models. For example, we discuss how it suggests a major simplification and modification of the recently proposed ekpyrotic scenario.}, - archivePrefix = {arXiv}, - eprint = {hep-th/0108187}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/khoury_et_al_2002_from_big_crunch_to_big_bang2.pdf;/home/riccardo/.local/share/zotero/storage/ZR347STA/0108187.html}, - number = {8} -} - @online{Kingma:2014:AutoEncodingVariationalBayes, title = {Auto-{{Encoding Variational Bayes}}}, author = {Kingma, Diederik P. and Welling, Max}, date = {2014}, - url = {http://arxiv.org/abs/1312.6114}, - urldate = {2020-10-10}, abstract = {How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions is two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.}, archivePrefix = {arXiv}, eprint = {1312.6114}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/kingma_welling_2014_auto-encoding_variational_bayes2.pdf;/home/riccardo/.local/share/zotero/storage/KYP8BISG/1312.html}, - keywords = {⛔ No DOI found}, - primaryClass = {cs, stat} + keywords = {⛔ No DOI found} } @online{Kingma:2017:AdamMethodStochastic, @@ -2773,12 +2111,10 @@ eprint = {1412.6980}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/kingma_ba_2017_adam3.pdf;/home/riccardo/.local/share/zotero/storage/9JQ8YQL7/1412.html}, - keywords = {⛔ No DOI found}, - primaryClass = {cs} + keywords = {⛔ No DOI found} } @online{Kingma:2017:AdamMethodStochastica, - ids = {Kingma:2017:AdamMethodStochastic}, title = {Adam: {{A Method}} for {{Stochastic Optimization}}}, shorttitle = {Adam}, author = {Kingma, Diederik P. and Ba, Jimmy}, @@ -2788,8 +2124,7 @@ eprint = {1412.6980}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/kingma_ba_2017_adam.pdf;/home/riccardo/.local/share/zotero/files/kingma_ba_2017_adam2.pdf;/home/riccardo/.local/share/zotero/storage/EYEANITG/1412.html}, - keywords = {⛔ No DOI found}, - version = {8} + keywords = {⛔ No DOI found} } @article{Kiritsis:1994:StringPropagationGravitational, @@ -2801,7 +2136,7 @@ volume = {320}, pages = {264--272}, issn = {03702693}, - doi = {10.1016/0370-2693(94)90655-6}, + doi = {10/bswvpn}, abstract = {The Conformal Field Theory of the current algebra of the centrally extended 2-d Euclidean group is analyzed. Its representations can be written in terms of four free fields (without background charge) with signature (\$-\$+++). We construct all irreducible representations of the current algebra with unitary base out of the free fields and their orbifolds. This is used to investigate the spectrum and scattering of strings moving in the background of a gravitational wave. We find that all the dynamics happens in the transverse space or the longitunal one but not both.}, archivePrefix = {arXiv}, eprint = {hep-th/9310202}, @@ -2819,7 +2154,7 @@ volume = {789}, pages = {438--443}, issn = {03702693}, - doi = {10.1016/j.physletb.2019.01.002}, + doi = {10/gg66kq}, archivePrefix = {arXiv}, eprint = {1809.02547}, eprinttype = {arxiv}, @@ -2837,8 +2172,7 @@ volume = {96}, pages = {066014}, issn = {2470-0010, 2470-0029}, - doi = {10.1103/PhysRevD.96.066014}, - annotation = {http://web.archive.org/web/20201007112546/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.066014}, + doi = {10/gcpp5w}, file = {/home/riccardo/.local/share/zotero/files/krefl_seong_2017_machine_learning_of_calabi-yau_volumes.pdf;/home/riccardo/.local/share/zotero/files/krefl_seong_2017_machine_learning_of_calabi-yau_volumes3.pdf}, keywords = {archived}, langid = {english}, @@ -2849,7 +2183,7 @@ title = {Complete Classification of Reflexive Polyhedra in Four Dimensions}, author = {Kreuzer, Maximilian and Skarke, Harald}, date = {2000}, - journaltitle = {Advances in Theoretical and Mathematical Physics}, + journaltitle = {Advances in theoretical and mathematical physics}, volume = {4}, pages = {1209--1230}, issn = {10950761, 10950753}, @@ -2863,19 +2197,6 @@ number = {6} } -@online{Krippendorf:2010:CambridgeLecturesSupersymmetry, - title = {Cambridge {{Lectures}} on {{Supersymmetry}} and {{Extra Dimensions}}}, - author = {Krippendorf, Sven and Quevedo, Fernando and Schlotterer, Oliver}, - date = {2010}, - abstract = {These lectures on supersymmetry and extra dimensions are aimed at finishing undergraduate and beginning postgraduate students with a background in quantum field theory and group theory. Basic knowledge in general relativity might be advantageous for the discussion of extra dimensions. This course was taught as a 24+1 lecture course in Part III of the Mathematical Tripos in recent years. The first six chapters give an introduction to supersymmetry in four spacetime dimensions, they fill about two thirds of the lecture notes and are in principle self-contained. The remaining two chapters are devoted to extra spacetime dimensions which are in the end combined with the concept of supersymmetry. Videos from the course lectured in 2006 can be found online at http://www.sms.cam.ac.uk/collection/659537 .}, - archivePrefix = {arXiv}, - eprint = {1011.1491}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/krippendorf_et_al_2010_cambridge_lectures_on_supersymmetry_and_extra_dimensions.pdf}, - keywords = {⛔ No DOI found}, - langid = {english} -} - @online{Krippendorf:2020:DetectingSymmetriesNeural, title = {Detecting {{Symmetries}} with {{Neural Networks}}}, author = {Krippendorf, Sven and Syvaeri, Marc}, @@ -2888,57 +2209,7 @@ keywords = {⛔ No DOI found} } -@article{Krishnan:2020:MachineLearningGauged, - title = {Machine {{Learning Gauged Supergravity}}}, - author = {Krishnan, Chethan and Mohan, Vyshnav and Ray, Soham}, - date = {2020}, - journaltitle = {Fortschritte der Physik}, - shortjournal = {Fortschr. Phys.}, - volume = {68}, - pages = {2000027}, - issn = {0015-8208, 1521-3978}, - doi = {10.1002/prop.202000027}, - archivePrefix = {arXiv}, - eprint = {2002.12927}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/krishnan_et_al_2020_machine_learning_gauged_supergravity.pdf}, - keywords = {archived}, - langid = {english}, - number = {5} -} - -@article{Lerche:1987:ChiralFourdimensionalHeterotic, - title = {Chiral Four-Dimensional Heterotic Strings from Self-Dual Lattices}, - author = {Lerche, Wolfgang and Lüst, Dieter and Schellekens, A. N.}, - date = {1987}, - journaltitle = {Nuclear Physics B}, - shortjournal = {Nuclear Physics B}, - volume = {287}, - pages = {477--507}, - issn = {05503213}, - doi = {10.1016/0550-3213(87)90115-5}, - file = {/home/riccardo/.local/share/zotero/files/lerche_et_al_1987_chiral_four-dimensional_heterotic_strings_from_self-dual_lattices.pdf}, - keywords = {archived}, - langid = {english} -} - -@book{Lista:2017:StatisticalMethodsData, - ids = {Lista:2017:StatisticalMethodsDataa,Lista:2017:StatisticalMethodsDatad}, - title = {Statistical {{Methods}} for {{Data Analysis}} in {{Particle Physics}}}, - author = {Lista, Luca}, - date = {2017}, - volume = {941}, - publisher = {{Springer International Publishing}}, - location = {{Cham}}, - doi = {10.1007/978-3-319-62840-0}, - file = {/home/riccardo/.local/share/zotero/files/lista_2017_statistical_methods_for_data_analysis_in_particle_physics7.pdf}, - isbn = {978-3-319-62839-4 978-3-319-62840-0}, - langid = {english}, - series = {Lecture {{Notes}} in {{Physics}}} -} - @article{Liu:2002:StringsTimeDependentOrbifold, - ids = {Liu:2002:StringsTimeDependent}, title = {Strings in a {{Time}}-{{Dependent Orbifold}}}, author = {Liu, Hong and Moore, Gregory and Seiberg, Nathan}, date = {2002}, @@ -2947,20 +2218,17 @@ volume = {2002}, pages = {045--045}, issn = {1126-6708}, - doi = {10.1088/1126-6708/2002/06/045}, + doi = {10/b2d2mj}, abstract = {We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. We quantize the theory both in light-cone gauge and covariantly. We also compute some tree and one loop amplitudes which exhibit interesting behavior near the singularity. Our results are compatible with the possibility that strings can pass through the singularity from the contracting to the expanding universe, but they also indicate the need for further study of certain divergent scattering amplitudes.}, - annotation = {ZSCC: 0000251}, archivePrefix = {arXiv}, eprint = {hep-th/0204168}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/liu_et_al_2002_strings_in_a_time-dependent_orbifold.pdf}, - issue = {06}, langid = {english}, - number = {RUNHETC-2002-11} + number = {06} } @article{Liu:2002:StringsTimeDependentOrbifolds, - ids = {Liu:2002:StringsTimeDependenta}, title = {Strings in {{Time}}-{{Dependent Orbifolds}}}, author = {Liu, Hong and Moore, Gregory and Seiberg, Nathan}, date = {2002}, @@ -2971,15 +2239,13 @@ issn = {1126-6708}, doi = {20050405175528}, abstract = {We continue and extend our earlier investigation “Strings in a Time-Dependent Orbifold” (hep-th/0204168). We formulate conditions for an orbifold to be amenable to perturbative string analysis and classify the low dimensional orbifolds satisfying these conditions. We analyze the tree and torus amplitudes of some of these orbifolds. The tree amplitudes exhibit a new kind of infrared divergences which are a result of some ultraviolet effects. These UV enhanced IR divergences can be interpreted as due to back reaction of the geometry. We argue that for this reason the three dimensional parabolic orbifold is not amenable to perturbation theory. Similarly, the smooth four dimensional null-brane tensored with sufficiently few noncompact dimensions also appears problematic. However, when the number of noncompact dimensions is sufficiently large perturbation theory in these time dependent backgrounds seems consistent.}, - annotation = {ZSCC: 0000208}, archivePrefix = {arXiv}, eprint = {hep-th/0206182}, eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/liu_et_al_2002_strings_in_time_dependent_orbifolds.pdf;/home/riccardo/.local/share/zotero/files/liu_et_al_2002_strings_in_time-dependent_orbifolds.pdf}, - issue = {10}, + file = {/home/riccardo/.local/share/zotero/files/liu_et_al_2002_strings_in_time_dependent_orbifolds.pdf}, keywords = {⚠️ Invalid DOI}, langid = {english}, - number = {RUNHETC-2002-19, NI-02014-MTH} + number = {10} } @article{Lust:2009:LHCStringHunter, @@ -2991,7 +2257,7 @@ volume = {808}, pages = {1--52}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2008.09.012}, + doi = {10/fdcxt4}, abstract = {The mass scale of fundamental strings can be as low as few TeV/c\^2 provided that spacetime extends into large extra dimensions. We discuss the phenomenological aspects of weakly coupled low mass string theory related to experimental searches for physics beyond the Standard Model at the Large Hadron Collider (LHC). We consider the extensions of the Standard Model based on open strings ending on D-branes, with gauge bosons due to strings attached to stacks of D-branes and chiral matter due to strings stretching between intersecting D-branes. We focus on the model-independent, universal features of low mass string theory. We compute, collect and tabulate the full-fledged string amplitudes describing all 2-{$>$}2 parton scattering subprocesses at the leading order of string perturbation theory. We cast our results in a form suitable for the implementation of stringy partonic cross sections in the LHC data analysis. The amplitudes involving four gluons as well as those with two gluons plus two quarks do not depend on the compactification details and are completely model-independent. They exhibit resonant behavior at the parton center of mass energies equal to the masses of Regge resonances. The existence of these resonances is the primary signal of string physics and should be easy to detect. On the other hand, the four-fermion processes like quark-antiquark scattering include also the exchanges of heavy Kaluza-Klein and winding states, whose details depend on the form of internal geometry. They could be used as ``precision tests'' in order to distinguish between various compactification scenarios.}, archivePrefix = {arXiv}, eprint = {0807.3333}, @@ -3009,7 +2275,7 @@ volume = {2009}, pages = {149--149}, issn = {1029-8479}, - doi = {10.1088/1126-6708/2009/03/149}, + doi = {10/bc336m}, archivePrefix = {arXiv}, eprint = {0904.4601}, eprinttype = {arxiv}, @@ -3022,7 +2288,7 @@ title = {Recent {{Progress}} in {{Calabi}}-{{Yauology}}}, author = {Lütken, Carsten Andrew}, date = {1988}, - doi = {10.1016/0920-5632(88)90380-5} + doi = {10/cw4cz2} } @article{Mallat:2016:UnderstandingDeepConvolutional, @@ -3032,8 +2298,7 @@ journaltitle = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {374}, pages = {20150203}, - publisher = {{The Royal Society Publishing}}, - doi = {10.1098/rsta.2015.0203}, + doi = {10/gcsgwj}, file = {/home/riccardo/.local/share/zotero/files/mallat_2016_understanding_deep_convolutional_networks2.pdf}, number = {2065} } @@ -3045,30 +2310,11 @@ journaltitle = {The Journal of Machine Learning Research}, volume = {17}, pages = {2853--2884}, - publisher = {{JMLR. org}}, keywords = {⛔ No DOI found}, number = {1} } -@article{Mehta:2019:HighbiasLowvarianceIntroduction, - title = {A High-Bias, Low-Variance Introduction to {{Machine Learning}} for Physicists}, - author = {Mehta, Pankaj and Bukov, Marin and Wang, Ching-Hao and Day, Alexandre G. R. and Richardson, Clint and Fisher, Charles K. and Schwab, David J.}, - date = {2019}, - journaltitle = {Physics Reports}, - shortjournal = {Physics Reports}, - volume = {810}, - pages = {1--124}, - issn = {03701573}, - doi = {10.1016/j.physrep.2019.03.001}, - abstract = {Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute. (Notebooks are available at https://physics.bu.edu/\textasciitilde pankajm/MLnotebooks.html )}, - archivePrefix = {arXiv}, - eprint = {1803.08823}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/mehta_et_al_2019_a_high-bias,_low-variance_introduction_to_machine_learning_for_physicists3.pdf;/home/riccardo/.local/share/zotero/storage/DVY32RS5/1803.html} -} - @inproceedings{Mockus:1975:BayesianMethodsSeeking, - ids = {Mockus:1975:BayesianMethodsSeekinga}, title = {On Bayesian Methods for Seeking the Extremum}, booktitle = {Optimization {{Techniques IFIP Technical Conference Novosibirsk}}, {{July}} 1–7, 1974}, author = {Močkus, J.}, @@ -3077,7 +2323,7 @@ pages = {400--404}, publisher = {{Springer}}, location = {{Berlin, Heidelberg}}, - doi = {10.1007/3-540-07165-2_55}, + doi = {10/dh23rk}, file = {/home/riccardo/.local/share/zotero/files/močkus_1975_on_bayesian_methods_for_seeking_the_extremum.pdf}, isbn = {978-3-540-37497-8}, langid = {english}, @@ -3102,7 +2348,7 @@ volume = {940}, pages = {113--129}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2019.01.013}, + doi = {10/gg66kz}, archivePrefix = {arXiv}, eprint = {1811.05993}, eprinttype = {arxiv}, @@ -3117,6 +2363,9 @@ author = {Ndirango, Anthony and Lee, Tyler}, date = {2019}, pages = {15862--15871}, + archivePrefix = {arXiv}, + eprint = {1910.13593}, + eprinttype = {arxiv}, keywords = {⛔ No DOI found} } @@ -3129,12 +2378,19 @@ volume = {240}, pages = {96--104}, issn = {03702693}, - doi = {10.1016/0370-2693(90)90415-3}, + doi = {10/fbgqqd}, keywords = {archived}, langid = {english}, number = {1-2} } +@article{Olver:2020:NISTDigitalLibrary, + title = {{{NIST}} Digital Library of Mathematical Functions}, + editor = {Olver, Frank W. J. and Olde Daalhuis, Adri and Lozier, Daniel W. and Schneider, Barry I. and Boisvert, Ronald F. and Clark, Charles W. and Miller, Bradley R. and Saunders, Bonita V. and Cohl, Howard S. and McClain, Maxine A.}, + date = {2020}, + url = {http://dlmf.nist.gov} +} + @article{Otsuka:2020:DeepLearningKmeans, title = {Deep Learning and K-Means Clustering in Heterotic String Vacua with Line Bundles}, author = {Otsuka, Hajime and Takemoto, Kenta}, @@ -3144,7 +2400,7 @@ volume = {2020}, pages = {47}, issn = {1029-8479}, - doi = {10.1007/JHEP05(2020)047}, + doi = {10/gg66k2}, archivePrefix = {arXiv}, eprint = {2003.11880}, eprinttype = {arxiv}, @@ -3162,7 +2418,7 @@ volume = {952}, pages = {114922}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2020.114922}, + doi = {10/ghf4n5}, archivePrefix = {arXiv}, eprint = {1910.13473}, eprinttype = {arxiv}, @@ -3180,7 +2436,7 @@ volume = {68}, pages = {2000032}, issn = {0015-8208, 1521-3978}, - doi = {10.1002/prop.202000032}, + doi = {10/ghf4n6}, archivePrefix = {arXiv}, eprint = {2003.01732}, eprinttype = {arxiv}, @@ -3199,7 +2455,7 @@ volume = {10}, pages = {516--520}, issn = {05503213}, - doi = {10.1016/0550-3213(69)90038-8}, + doi = {10/chp79v}, file = {/home/riccardo/.local/share/zotero/files/paton_chan_hong-mo_1969_generalized_veneziano_model_with_isospin.pdf}, keywords = {archived}, langid = {english}, @@ -3237,9 +2493,11 @@ volume = {793}, pages = {211--245}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2007.10.002}, + doi = {10/bh6q64}, abstract = {We derive boundary states which describe configurations of multiple parallel branes with arbitrary open string states interactions in bosonic string theory. This is obtained by a careful discussion of the factorization of open/closed string states amplitudes taking care of cycles needed by ensuring vertexes commutativity: in particular the discussion reveals that already at the tree level open string knows of the existence of closed string. We also give a formal expression for computing pure closed string amplitudes using the open string formalism.}, - annotation = {ZSCC: 0000011}, + archivePrefix = {arXiv}, + eprint = {hep-th/0310027}, + eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/pesando_2008_multi-branes_boundary_states_with_open_string_interactions.pdf}, number = {1-2} } @@ -3253,7 +2511,7 @@ volume = {2010}, pages = {64}, issn = {1029-8479}, - doi = {10.1007/JHEP02(2010)064}, + doi = {10/fr82w9}, abstract = {We discuss carefully the vertices which describe the dipole open strings and closed strings on a D-brane with magnetic flux on a torus. Translation invariance along closed cycles forces surprisingly closed string vertices written in open string formalism to acquire Chan-Paton like matrices. Moreover the one loop amplitudes have a single trace for the part of gauge group with the magnetic flux. These peculiarities are also required by consistency of the action of T-duality in the open string sector. In this way we can show to all orders in perturbation theory the equivalence of the T-dual open string theories, gravitational interactions included. We provide also a new and direct derivation of the bosonic boundary state in presence of constant magnetic and Kalb-Ramond background based on Sciuto-Della Selva-Saito vertex formalism.}, archivePrefix = {arXiv}, eprint = {0910.2576}, @@ -3271,8 +2529,7 @@ eprint = {1107.5525}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/pesando_2011_the_generating_function_of_amplitudes_with_n_twisted_and_m_untwisted_states.pdf}, - keywords = {⛔ No DOI found}, - primaryClass = {hep-th} + keywords = {⛔ No DOI found} } @article{Pesando:2011:StringsArbitraryConstant, @@ -3284,7 +2541,7 @@ volume = {2011}, pages = {138}, issn = {1029-8479}, - doi = {10.1007/JHEP06(2011)138}, + doi = {10/ddhtfm}, abstract = {We quantize the open string in an arbitrary constant magnetic field with a non factorized metric on a torus. We then discuss carefully the vertexes which describe the emission of dipole open strings and closed strings in the non compact limit. Finally we compute various stringy form factors which in the compact case induces a Kaehler and complex structure dependence and suppression of some amplitudes with KK states.}, archivePrefix = {arXiv}, eprint = {1101.5898}, @@ -3294,7 +2551,6 @@ } @article{Pesando:2012:GreenFunctionsTwist, - ids = {Pesando:2013:GreenFunctionsTwist}, title = {Green Functions and Twist Correlators for {{N}} Branes at Angles}, author = {Pesando, Igor}, date = {2012}, @@ -3302,16 +2558,13 @@ volume = {866}, pages = {87--123}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2012.08.016}, + doi = {10/gf66ch}, abstract = {We compute the Green functions and correlator functions for N twist fields for branes at angles on T\^2 and we show that there are N-2 different configurations labeled by an integer M which is roughly associated with the number of obtuse angles of the configuration. In order to perform this computation we use a SL(2,R) invariant formulation and geometric constraints instead of Pochammer contours. In particular the M=1 or M=N-1 amplitude can be expressed without using transcendental functions. We determine the amplitudes normalization from N -\textbackslash textgreater N-1 reduction without using the factorization into the untwisted sector. Both the amplitudes normalization and the OPE of two twist fields are unique (up to one constant) when the \$\textbackslash backslash\$epsilon \textbackslash textless-\textbackslash textgreater 1-\$\textbackslash backslash\$epsilon symmetry is imposed. For consistency we find also an infinite number of relations among Lauricella hypergeometric functions.}, - annotation = {ZSCC: 0000000[s0]}, archivePrefix = {arXiv}, eprint = {1206.1431}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/pesando_2012_green_functions_and_twist_correlators_for_$n$_branes_at_angles.pdf}, - issue = {2}, - number = {DFTT-6-2012}, - primaryClass = {hep-th} + number = {2} } @article{Pesando:2013:LightConeQuantization, @@ -3323,7 +2576,7 @@ volume = {876}, pages = {1--15}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2013.07.022}, + doi = {10/f5cppv}, abstract = {We quantize the bosonic part of the D1 string with closed boundary conditions on the light cone and we consider the U(1) worldsheet gauge field a dynamical variable. We compute also 3-Reggeon vertex by the overlapping technique. We find that the Fock space is the sum of sectors characterized by the momentum of the U(1) Wilson line and that these sectors do not interact among them. Each sector has exactly the same spectrum of the usual bosonic string when expressed in properly sector dependent rescaled variables. Rescaling is forced by factorization of the string amplitudes. We are also able to determine the relative string coupling constant of the different sectors. It follows a somewhat unexpected picture in which the effective action is always the same independently on the sector but string amplitudes are only the same when expressed in sector dependent rescaled variables.}, archivePrefix = {arXiv}, eprint = {1305.2710}, @@ -3341,7 +2594,7 @@ volume = {889}, pages = {120--155}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2014.10.005}, + doi = {10/f6vwhg}, abstract = {We study the canonical quantization of a bosonic string in presence of N twist fields. This generalizes the quantization of the twisted string in two ways: the in and out states are not necessarily twisted and the number of twist fields N can be bigger than 2. In order to quantize the theory we need to find the normal modes. Then we need to define a product between two modes which is conserved. Because of this we need to use the Klein-Gordon product and to separate the string coordinate into the classical and the quantum part. The quantum part has different boundary conditions than the original string coordinates but these boundary conditions are precisely those which make the operator describing the equation of motion self adjoint. The splitting of the string coordinates into a classical and quantum part allows the formulation of an improved overlap principle. Using this approach we then proceed in computing the generating function for the generic correlator with L untwisted operators and N (excited) twist fields for branes at angles. We recover as expected the results previously obtained using the path integral. This construction explains why these correlators}, archivePrefix = {arXiv}, eprint = {1407.4627}, @@ -3350,7 +2603,6 @@ } @article{Pesando:2014:CorrelatorsArbitraryUntwisted, - ids = {Pesando:2014:CorrelatorsArbitraryUntwisteda}, title = {Correlators of Arbitrary Untwisted Operators and Excited Twist Operators for {{N}} Branes at Angles}, author = {Pesando, Igor}, date = {2014}, @@ -3358,33 +2610,28 @@ volume = {886}, pages = {243--287}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2014.06.010}, + doi = {10/gf66cg}, abstract = {We compute the generic correlator with L untwisted operators and N (excited) twist fields for branes at angles on T\^2 and show that it is given by a generalization of the Wick theorem. We give also the recipe to compute efficiently the generic OPE between an untwisted operator and an excited twisted state.}, - annotation = {ZSCC: 0000012}, archivePrefix = {arXiv}, eprint = {1401.6797}, eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/pesando_2014_correlators_of_arbitrary_untwisted_operators_and_excited_twist_operators_for_n2.pdf}, - primaryClass = {hep-th} + file = {/home/riccardo/.local/share/zotero/files/pesando_2014_correlators_of_arbitrary_untwisted_operators_and_excited_twist_operators_for_n2.pdf} } @article{Pesando:2016:FullyStringyComputation, - ids = {Pesando:2016:FullyStringyComputationa}, - title = {Towards a Fully Stringy Computation of {{Yukawa}} Couplings on Non-Factorized Tori and Non-Abelian Twist Correlators ({{I}}): {{The}} Classical Solution and Action}, + title = {Towards a Fully Stringy Computation of {{Yukawa}} Couplings on Non-Factorized Tori and Non-{{Abelian}} Twist Correlators ({{I}}): {{The}} Classical Solution and Action}, author = {Pesando, Igor}, date = {2016}, journaltitle = {Nuclear Physics B}, volume = {910}, pages = {618--664}, issn = {05503213}, - doi = {10.1016/j.nuclphysb.2016.06.013}, + doi = {10/f82v5m}, abstract = {We consider the simplest possible setting of non-abelian twist fields which corresponds to SU(2) monodromies. We first review the theory of hypergeometric function and of the solutions of the most general Fuchsian second order equation with three singularities. Then we solve the problem of writing the general solution with prescribed U(2) monodromies. We use this result to compute the classical string solution corresponding to three D2 branes in R4. Despite the fact that the configuration is supersymmetric the classical string solution is not holomorphic. Using the equation of motion and not the KLT approach we give a very simple expression for the classical action of the string. We find that the classical action is not proportional to the area of the triangle determined by the branes intersection points since the solution is not holomorphic. Phenomenologically this means that the Yukawa couplings for these supersymmetric configurations on non-factorized tori are suppressed with respect to the factorized case.}, - annotation = {ZSCC: 0000003}, archivePrefix = {arXiv}, eprint = {1512.07920}, eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/pesando_2016_towards_a_fully_stringy_computation_of_yukawa_couplings_on_non_factorized_tori.pdf}, - primaryClass = {hep-th} + file = {/home/riccardo/.local/share/zotero/files/pesando_2016_towards_a_fully_stringy_computation_of_yukawa_couplings_on_non_factorized_tori.pdf} } @article{Petersen:1989:CovariantSuperreggeonCalculus, @@ -3396,7 +2643,7 @@ volume = {317}, pages = {109--146}, issn = {05503213}, - doi = {10.1016/0550-3213(89)90564-6}, + doi = {10/bpfrkw}, keywords = {archived}, langid = {english}, number = {1} @@ -3410,7 +2657,7 @@ volume = {75}, pages = {4724--4727}, issn = {00319007}, - doi = {10.1103/physrevlett.75.4724}, + doi = {10/bxcwrv}, abstract = {We show that Dirichlet-branes, extended objects defined by mixed Dirichlet-Neumann boundary conditions in string theory, break half of the supersymmetries of the type∼II superstring and carry a complete set of electric and magnetic Ramond-Ramond charges. We also find that the product of the electric and magnetic charges is a single Dirac unit, and that the quantum of charge takes the value required by string duality. This is strong evidence that the Dirchlet-branes are intrinsic to type II string theory and are the Ramond-Ramond sources required by string duality. We also note the existence of a previously overlooked 9-form potential in the IIa string, which gives rise to an effective cosmological constant of undetermined magnitude.}, archivePrefix = {arXiv}, eprint = {hep-th/9510017}, @@ -3439,9 +2686,9 @@ date = {1998}, volume = {1}, publisher = {{Cambridge University Press}}, - doi = {10.1017/CBO9780511816079}, + url = {https://www.cambridge.org/academic/subjects/physics/theoretical-physics-and-mathematical-physics/string-theory-volume-1}, file = {/home/riccardo/.local/share/zotero/files/polchinski_1998_string_theory.pdf}, - isbn = {978-0-521-67227-6 978-0-521-63303-1 978-0-511-81607-9}, + isbn = {978-0-521-67227-6}, keywords = {archived} } @@ -3451,9 +2698,9 @@ date = {1998}, volume = {2}, publisher = {{Cambridge University Press}}, - doi = {10.1017/CBO9780511618123}, + url = {https://www.cambridge.org/academic/subjects/physics/theoretical-physics-and-mathematical-physics/string-theory-volume-2}, file = {/home/riccardo/.local/share/zotero/files/polchinski_1998_string_theory2.pdf}, - isbn = {978-0-521-63304-8 978-0-521-67228-3 978-0-511-61812-3}, + isbn = {978-0-521-63304-8}, keywords = {archived} } @@ -3466,7 +2713,7 @@ volume = {103}, pages = {207--210}, issn = {03702693}, - doi = {10.1016/0370-2693(81)90743-7}, + doi = {10/cq538n}, file = {/home/riccardo/.local/share/zotero/files/polyakov_1981_quantum_geometry_of_bosonic_strings2.pdf}, keywords = {archived}, langid = {english}, @@ -3474,20 +2721,17 @@ } @article{Quinlan:1986:InductionDecisionTrees, - ids = {Quinlan:1986:InductionDecisionTreesa}, title = {Induction of Decision Trees}, author = {Quinlan, John R.}, date = {1986}, - journaltitle = {Machine Learning}, + journaltitle = {Machine learning}, shortjournal = {Mach Learn}, volume = {1}, pages = {81--106}, - publisher = {{Springer}}, issn = {1573-0565}, - doi = {10.1007/bf00116251}, + doi = {10/ctd6mv}, abstract = {The technology for building knowledge-based systems by inductive inference from examples has been demonstrated successfully in several practical applications. This paper summarizes an approach to synthesizing decision trees that has been used in a variety of systems, and it describes one such system, ID3, in detail. Results from recent studies show ways in which the methodology can be modified to deal with information that is noisy and/or incomplete. A reported shortcoming of the basic algorithm is discussed and two means of overcoming it are compared. The paper concludes with illustrations of current research directions.}, file = {/home/riccardo/.local/share/zotero/files/quinlan_1986_induction_of_decision_trees.pdf}, - keywords = {❓ Multiple DOI}, langid = {english}, number = {1} } @@ -3496,15 +2740,12 @@ title = {Stochastic {{Backpropagation}} and {{Approximate Inference}} in {{Deep Generative Models}}}, author = {Rezende, Danilo Jimenez and Mohamed, Shakir and Wierstra, Daan}, date = {2014}, - url = {http://arxiv.org/abs/1401.4082}, - urldate = {2020-10-10}, abstract = {We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a recognition model to represent approximate posterior distributions, and that acts as a stochastic encoder of the data. We develop stochastic back-propagation -- rules for back-propagation through stochastic variables -- and use this to develop an algorithm that allows for joint optimisation of the parameters of both the generative and recognition model. We demonstrate on several real-world data sets that the model generates realistic samples, provides accurate imputations of missing data and is a useful tool for high-dimensional data visualisation.}, archivePrefix = {arXiv}, eprint = {1401.4082}, eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/rezende_et_al_2014_stochastic_backpropagation_and_approximate_inference_in_deep_generative_models2.pdf;/home/riccardo/.local/share/zotero/storage/HKC6H5VK/1401.html}, - keywords = {⛔ No DOI found}, - primaryClass = {cs, stat} + keywords = {⛔ No DOI found} } @article{Rudolph:1994:ConvergenceAnalysisCanonical, @@ -3514,7 +2755,7 @@ journaltitle = {IEEE transactions on neural networks}, volume = {5}, pages = {96--101}, - doi = {10.1109/72.265964}, + doi = {10/fw8z8k}, file = {/home/riccardo/.local/share/zotero/files/rudolph_1994_convergence_analysis_of_canonical_genetic_algorithms3.pdf}, number = {1} } @@ -3528,7 +2769,7 @@ volume = {2017}, pages = {38}, issn = {1029-8479}, - doi = {10.1007/JHEP08(2017)038}, + doi = {10/gbss9c}, archivePrefix = {arXiv}, eprint = {1706.07024}, eprinttype = {arxiv}, @@ -3546,7 +2787,7 @@ volume = {839}, pages = {1--117}, issn = {03701573}, - doi = {10.1016/j.physrep.2019.09.005}, + doi = {10/ggwkvm}, file = {/home/riccardo/.local/share/zotero/files/ruehle_2020_data_science_applications_to_string_theory5.pdf}, keywords = {archived}, langid = {english} @@ -3558,61 +2799,22 @@ date = {1986}, volume = {323}, pages = {533--536}, - publisher = {{Nature Publishing Group}}, - doi = {10.1038/323533a0}, + doi = {10/cvjdpk}, file = {/home/riccardo/.local/share/zotero/files/rumelhart_et_al_1986_learning_representations_by_back-propagating_errors2.pdf}, number = {6088} } -@inproceedings{Salimans:2015:MarkovChainMonte, - title = {Markov Chain Monte Carlo and Variational Inference: {{Bridging}} the Gap}, - booktitle = {International Conference on Machine Learning}, - author = {Salimans, Tim and Kingma, Diederik and Welling, Max}, - date = {2015}, - pages = {1218--1226}, - file = {/home/riccardo/.local/share/zotero/files/salimans_et_al_2015_markov_chain_monte_carlo_and_variational_inference.pdf}, - keywords = {⛔ No DOI found} -} - @inproceedings{Scarselli:2004:GraphicalbasedLearningEnvironments, title = {Graphical-Based Learning Environments for Pattern Recognition}, booktitle = {Joint {{IAPR}} International Workshops on Statistical Techniques in Pattern Recognition ({{SPR}}) and Structural and Syntactic Pattern Recognition ({{SSPR}})}, author = {Scarselli, Franco and Tsoi, Ah Chung and Gori, Marco and Hagenbuchner, Markus}, date = {2004}, pages = {42--56}, - doi = {10.1007/978-3-540-27868-9_4}, + doi = {10/dtgbgk}, file = {/home/riccardo/.local/share/zotero/files/scarselli_et_al_2004_graphical-based_learning_environments_for_pattern_recognition3.pdf}, isbn = {978-3-540-22570-6 978-3-540-27868-9} } -@online{Schellekens:2017:BigNumbersString, - title = {Big {{Numbers}} in {{String Theory}}}, - author = {Schellekens, A. N.}, - date = {2017}, - abstract = {This paper contains some personal reflections on several computational contributions to what is now known as the "String Theory Landscape". It consists of two parts. The first part concerns the origin of big numbers, and especially the number \$10\^\{1500\}\$ that appeared in work on the covariant lattice construction (with W. Lerche and D. Luest). This part contains some new results. I correct a huge but inconsequential error, discuss some more accurate estimates, and compare with the counting for free fermion constructions. In particular I prove that the latter only provide an exponentially small fraction of all even self-dual lattices for large lattice dimensions. The second part of the paper concerns dealing with big numbers, and contains some lessons learned from various vacuum scanning projects.}, - archivePrefix = {arXiv}, - eprint = {1601.02462}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/schellekens_2017_big_numbers_in_string_theory.pdf;/home/riccardo/.local/share/zotero/storage/EJQ3TBMK/1601.html}, - keywords = {⛔ No DOI found}, - primaryClass = {hep-th} -} - -@article{Schwarz:1973:EvaluationDualFermion, - title = {Evaluation of Dual Fermion Amplitudes}, - author = {Schwarz, John H. and Wu, C. C.}, - date = {1973}, - journaltitle = {Physics Letters B}, - shortjournal = {Physics Letters B}, - volume = {47}, - pages = {453--456}, - issn = {03702693}, - doi = {10.1016/0370-2693(73)90112-3}, - keywords = {archived}, - langid = {english}, - number = {5} -} - @article{Sciuto:1969:GeneralVertexFunction, title = {The General Vertex Function in Dual Resonance Models}, author = {Sciuto, Stefano}, @@ -3622,7 +2824,7 @@ volume = {2}, pages = {411--418}, issn = {0375-930X, 1827-613X}, - doi = {10.1007/BF02755622}, + doi = {10/drsft8}, file = {/home/riccardo/.local/share/zotero/files/sciuto_1969_the_general_vertex_function_in_dual_resonance_models5.pdf}, langid = {english}, number = {9} @@ -3635,14 +2837,12 @@ journaltitle = {Proceedings of the IEEE}, volume = {104}, pages = {148--175}, - publisher = {{IEEE}}, - doi = {10.1109/JPROC.2015.2494218}, + doi = {10/f75n9c}, file = {/home/riccardo/.local/share/zotero/files/shahriari_et_al_2015_taking_the_human_out_of_the_loop.pdf}, number = {1} } @article{Sheikh-Jabbari:1998:ClassificationDifferentBranes, - ids = {SheikhJabbari:1998:ClassificationDifferentBranes}, title = {Classification of {{Different Branes}} at {{Angles}}}, author = {Sheikh-Jabbari, Mohammad M.}, date = {1998}, @@ -3651,7 +2851,7 @@ volume = {420}, pages = {279--284}, issn = {03702693}, - doi = {10.1016/S0370-2693(97)01550-5}, + doi = {10/dbhwc6}, abstract = {In this paper, we consider two D-branes rotated with respect to each other, and argue that in this way one can find brane configurations preserving \$\{1 \textbackslash f 16\}\$ of SUSY. Also we classify different brane configurations preserving \$\{1 \textbackslash f 2\}\$, \$\{1 \textbackslash f 4\}\$, \$\{3 \textbackslash f 16\}\$,\$\{1 \textbackslash f 8\}\$, \$\{1 \textbackslash f 16\}\$ of SUSY.}, archivePrefix = {arXiv}, eprint = {hep-th/9710121}, @@ -3665,7 +2865,9 @@ author = {Skiena, Steven S.}, date = {2017}, publisher = {{Springer}}, - file = {/home/riccardo/.local/share/zotero/files/skiena_2017_the_data_science_design_manual.pdf} + url = {https://link.springer.com/book/10.1007/978-3-319-55444-0}, + file = {/home/riccardo/.local/share/zotero/files/skiena_2017_the_data_science_design_manual.pdf}, + isbn = {978-3-319-55444-0} } @inproceedings{Snoek:2012:PracticalBayesianOptimization, @@ -3686,14 +2888,13 @@ volume = {186}, pages = {321--327}, issn = {03702693}, - doi = {10.1016/0370-2693(87)90302-9}, + doi = {10/dnd5gz}, keywords = {archived}, langid = {english}, number = {3-4} } @article{Srivastava:2014:DropoutSimpleWay, - ids = {Srivastava:2014:DropoutSimpleWaya}, title = {Dropout: {{A Simple Way}} to {{Prevent Neural Networks}} from {{Overfitting}}}, shorttitle = {Dropout}, author = {Srivastava, Nitish and Hinton, Geoffrey and Krizhevsky, Alex and Sutskever, Ilya and Salakhutdinov, Ruslan}, @@ -3702,7 +2903,6 @@ volume = {15}, pages = {1929--1958}, url = {http://jmlr.org/papers/v15/srivastava14a.html}, - urldate = {2020-02-19}, file = {/home/riccardo/.local/share/zotero/files/srivastava_et_al_2014_dropout.pdf;/home/riccardo/.local/share/zotero/files/srivastava_et_al_2014_dropout2.pdf}, keywords = {⛔ No DOI found} } @@ -3717,7 +2917,7 @@ volume = {07}, pages = {3059--3070}, issn = {0217-7323, 1793-6632}, - doi = {10.1142/S0217732392002457}, + doi = {10/d9jgv3}, abstract = {The three point correlation functions with twist fields are determined for bosonic \$Z\_N\$ orbifolds. Both the choice of the modular background (compatible with the twist) and of the (higher) twisted sectors involved are fully general. We point out a necessary restriction on the set of instantons contributing to twist field correlation functions not obtained in previous calculations. Our results show that the theory is target space duality invariant.}, archivePrefix = {arXiv}, eprint = {hep-th/9204037}, @@ -3773,52 +2973,6 @@ keywords = {⛔ No DOI found} } -@article{Tan:2019:DeepLearningHolographic, - title = {Deep Learning the Holographic Black Hole with Charge}, - author = {Tan, Jing and Chen, Chong-Bin}, - date = {2019}, - journaltitle = {International Journal of Modern Physics D}, - shortjournal = {Int. J. Mod. Phys. D}, - volume = {28}, - pages = {1950153}, - issn = {0218-2718, 1793-6594}, - doi = {10.1142/S0218271819501530}, - abstract = {We use the deep learning algorithm to learn the Reissner–Nordström (RN) black hole metric by building a deep neural network. Plenty of data are determined in boundary of AdS and we propagate them to the black hole horizon through AdS metric and equation of motion (e.o.m). We label these data according to the values near the horizon, and together with initial data they constitute a data set. Then we construct corresponding deep neural network and train it with the data set to obtain the Reissner–Nordström (RN) black hole metric. Finally, we discuss the effects of learning rate, batch-size and initialization on the training process.}, - archivePrefix = {arXiv}, - eprint = {1908.01470}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/tan_chen_2019_deep_learning_the_holographic_black_hole_with_charge2.pdf}, - keywords = {archived}, - langid = {english}, - number = {12} -} - -@online{Taylor:2003:LecturesDbranesTachyon, - title = {Lectures on {{D}}-Branes, Tachyon Condensation, and String Field Theory}, - author = {Taylor, Washington}, - date = {2003}, - abstract = {These lectures provide an introduction to the subject of tachyon condensation in the open bosonic string. The problem of tachyon condensation is first described in the context of the low-energy Yang-Mills description of a system of multiple D-branes, and then using the language of string field theory. An introduction is given to Witten's cubic open bosonic string field theory. The Sen conjectures on tachyon condensation in open bosonic string field theory are introduced, and evidence confirming these conjectures is reviewed.}, - archivePrefix = {arXiv}, - eprint = {hep-th/0301094}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/taylor_2003_lectures_on_d-branes,_tachyon_condensation,_and_string_field_theory.pdf}, - keywords = {⛔ No DOI found} -} - -@article{Taylor:2004:DBranesTachyonsString, - title = {D-{{Branes}}, {{Tachyons}}, and {{String Field Theory}}}, - author = {Taylor, Washington and Zwiebach, Barton}, - date = {2004}, - journaltitle = {Strings, Branes and Extra Dimensions}, - pages = {641--760}, - doi = {10.1142/9789812702821_0012}, - abstract = {In these notes we provide a pedagogical introduction to the subject of tachyon condensation in Witten's cubic bosonic open string field theory. We use both the low-energy Yang-Mills description and the language of string field theory to explain the problem of tachyon condensation on unstable D-branes. We give a self-contained introduction to open string field theory using both conformal field theory and overlap integrals. Our main subjects are the Sen conjectures on tachyon condensation in open string field theory and the evidence that supports these conjectures. We conclude with a discussion of vacuum string field theory and projectors of the star-algebra of open string fields. We comment on the possible role of string field theory in the construction of a nonperturbative formulation of string theory that captures all possible string backgrounds.}, - archivePrefix = {arXiv}, - eprint = {hep-th/0311017}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/taylor_zwiebach_2004_d-branes,_tachyons,_and_string_field_theory.pdf} -} - @article{Taylor:2015:FtheoryGeometryMost, title = {The {{F}}-Theory Geometry with Most Flux Vacua}, author = {Taylor, Washington and Wang, Yi-Nan}, @@ -3828,7 +2982,7 @@ volume = {2015}, pages = {1--21}, issn = {1029-8479}, - doi = {10.1007/JHEP12(2015)164}, + doi = {10/ghf4n7}, archivePrefix = {arXiv}, eprint = {1511.03209}, eprinttype = {arxiv}, @@ -3846,7 +3000,7 @@ volume = {2018}, pages = {111}, issn = {1029-8479}, - doi = {10.1007/JHEP01(2018)111}, + doi = {10/ghf4n8}, archivePrefix = {arXiv}, eprint = {1710.11235}, eprinttype = {arxiv}, @@ -3865,7 +3019,7 @@ pages = {151--260}, publisher = {{Academic Press}}, location = {{Boston}}, - doi = {10.1016/B978-1-59749-272-0.50006-2}, + url = {http://www.sciencedirect.com/science/article/pii/B9781597492720500062}, isbn = {978-1-59749-272-0} } @@ -3876,27 +3030,13 @@ journaltitle = {Physics Letters B}, volume = {198}, pages = {61--63}, - doi = {10.1016/0370-2693(87)90159-6}, + doi = {10/fkzsbw}, abstract = {The scattering process of two pointlike particles at CM energies in the order of Planck units or beyond, is very well calculable using known laws of physics, because graviton exchange dominates over all other interaction processes. At energies much higher than the Planck mass black hole production sets in, accompanied by coherent emission of real gravitons.}, - annotation = {ZSCC: 0000000[s0]}, file = {/home/riccardo/.local/share/zotero/files/'t_hooft_1987_graviton_dominance_in_ultra-high-energy_scattering.pdf}, number = {1}, options = {useprefix=true} } -@online{tHooft:2009:DimensionalReductionQuantum, - title = {Dimensional {{Reduction}} in {{Quantum Gravity}}}, - author = {'t Hooft, Gerard}, - date = {2009}, - abstract = {The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable degrees of freedom can best be described as if they were Boolean variables defined on a two-dimensional lattice, evolving with time. This observation, deduced from not much more than unitarity, entropy and counting arguments, implies severe restrictions on possible models of quantum gravity. Using cellular automata as an example it is argued that this dimensional reduction implies more constraints than the freedom we have in constructing models. This is the main reason why so-far no completely consistent mathematical models of quantum black holes have been found. Essay dedicated to Abdus Salam.}, - archivePrefix = {arXiv}, - eprint = {gr-qc/9310026}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/hooft_2009_dimensional_reduction_in_quantum_gravity.pdf}, - keywords = {⛔ No DOI found}, - options = {useprefix=true} -} - @inproceedings{Thrun:1996:LearningNthThing, title = {Is Learning the N-Th Thing Any Easier than Learning the First?}, booktitle = {Advances in Neural Information Processing Systems}, @@ -3910,6 +3050,7 @@ title = {Efficient {{Object Localization Using Convolutional Networks}}}, author = {Tompson, Jonathan and Goroshin, Ross and Jain, Arjun and LeCun, Yann and Bregler, Christopher}, date = {2015}, + doi = {10/ggtmv2}, abstract = {Recent state-of-the-art performance on human-body pose estimation has been achieved with Deep Convolutional Networks (ConvNets). Traditional ConvNet architectures include pooling and sub-sampling layers which reduce computational requirements, introduce invariance and prevent over-training. These benefits of pooling come at the cost of reduced localization accuracy. We introduce a novel architecture which includes an efficient `position refinement' model that is trained to estimate the joint offset location within a small region of the image. This refinement model is jointly trained in cascade with a state-of-the-art ConvNet model to achieve improved accuracy in human joint location estimation. We show that the variance of our detector approaches the variance of human annotations on the FLIC dataset and outperforms all existing approaches on the MPII-human-pose dataset.}, archivePrefix = {arXiv}, eprint = {1411.4280}, @@ -3926,7 +3067,10 @@ volume = {20}, pages = {S373-S393}, issn = {0264-9381, 1361-6382}, - doi = {10.1088/0264-9381/20/12/303}, + doi = {10/cr8vtd}, + archivePrefix = {arXiv}, + eprint = {hep-th/0301032}, + eprinttype = {arxiv}, file = {/home/riccardo/.local/share/zotero/files/uranga_2003_chiral_four-dimensional_string_compactifications_with_intersecting_d-branes.pdf}, number = {12} } @@ -3948,35 +3092,17 @@ journaltitle = {Computing in Science Engineering}, volume = {13}, pages = {22--30}, - doi = {10.1109/MCSE.2011.37}, + doi = {10/d8k4p9}, file = {/home/riccardo/.local/share/zotero/files/der_walt_et_al_2011_the_numpy_array.pdf}, number = {2}, options = {useprefix=true} } -@article{Wang:2018:LearningNonHiggsableGauge, - title = {Learning Non-{{Higgsable}} Gauge Groups in {{4D F}}-Theory}, - author = {Wang, Yi-Nan and Zhang, Zhibai}, - date = {2018}, - journaltitle = {Journal of High Energy Physics}, - shortjournal = {J. High Energ. Phys.}, - volume = {2018}, - pages = {9}, - issn = {1029-8479}, - doi = {10.1007/JHEP08(2018)009}, - archivePrefix = {arXiv}, - eprint = {1804.07296}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/wang_zhang_2018_learning_non-higgsable_gauge_groups_in_4d_f-theory3.pdf}, - langid = {english}, - number = {8} -} - @software{Waskom:2020:MwaskomSeabornV0, title = {Mwaskom/Seaborn: V0.11.0 ({{September}} 2020)}, author = {Waskom, Michael and Botvinnik, Olga and Gelbart, Maoz and Ostblom, Joel and Hobson, Paul and Lukauskas, Saulius and Gemperline, David C and Augspurger, Tom and Halchenko, Yaroslav and Warmenhoven, Jordi and Cole, John B. and de Ruiter, Julian and Vanderplas, Jake and Hoyer, Stephan and Pye, Cameron and Miles, Alistair and Swain, Corban and Meyer, Kyle and Martin, Marcel and Bachant, Pete and Quintero, Eric and Kunter, Gero and Villalba, Santi and {Brian} and Fitzgerald, Clark and Evans, C.G. and Williams, Mike Lee and O'Kane, Drew and Yarkoni, Tal and Brunner, Thomas}, date = {2020}, - doi = {10.5281/zenodo.4019146; http://web.archive.org/web/20201007135547/https://zenodo.org/record/4019146}, + url = {https://zenodo.org/record/4019146}, keywords = {archived}, options = {useprefix=true}, organization = {{Zenodo}}, @@ -3990,7 +3116,7 @@ editor = {van der Walt, Stéfan and {Jarrod Millman}}, date = {2010}, pages = {56--61}, - doi = {10.25080/Majora-92bf1922-00a}, + doi = {10/ggr6q3}, file = {/home/riccardo/.local/share/zotero/files/wes_mckinney_2010_data_structures_for_statistical_computing_in_python3.pdf}, options = {useprefix=true} } @@ -4007,18 +3133,6 @@ keywords = {⛔ No DOI found} } -@online{Yan:2020:DeepLearningBlack, - title = {Deep {{Learning}} Black Hole Metrics from Shear Viscosity}, - author = {Yan, Yu-Kun and Wu, Shao-Feng and Ge, Xian-Hui and Tian, Yu}, - date = {2020}, - abstract = {Based on the AdS/CFT correspondence, we build up a deep neural network to learn the black-hole metrics from the complex frequency-dependent shear viscosity. The network architecture provides a discretized representation of the holographic renormalization group flow of the shear viscosity and is applicable for a large class of strongly coupled field theories. Given the existence of the horizon and guided by the smoothness of spacetimes, we show that the Schwarzschild and Reissner-Nordstr\textbackslash "\{o\}m metrics can be learned accurately. Moreover, we illustrate that the generalization ability of the deep neural network can be excellent, which indicates that using the black hole spacetime as a hidden data structure, a wide spectrum of the shear viscosity can be generated from a narrow frequency range. Our work might not only suggest a data-driven way to study holographic transports but also shed new light on the emergence mechanism of black hole spacetimes from field theories.}, - archivePrefix = {arXiv}, - eprint = {2004.12112}, - eprinttype = {arxiv}, - file = {/home/riccardo/.local/share/zotero/files/yan_et_al_2020_deep_learning_black_hole_metrics_from_shear_viscosity2.pdf;/home/riccardo/.local/share/zotero/storage/SHKSTBVX/2004.html}, - keywords = {⛔ No DOI found} -} - @article{Yau:1977:CalabiConjectureNew, title = {Calabi's Conjecture and Some New Results in Algebraic Geometry}, author = {Yau, Shing-Tung}, @@ -4028,7 +3142,7 @@ volume = {74}, pages = {1798--1799}, issn = {0027-8424, 1091-6490}, - doi = {10.1073/pnas.74.5.1798}, + doi = {10/cbzd2h}, file = {/home/riccardo/.local/share/zotero/files/yau_1977_calabi's_conjecture_and_some_new_results_in_algebraic_geometry2.pdf}, langid = {english}, number = {5} @@ -4039,7 +3153,9 @@ author = {Zheng, Alice and Casari, Amanda}, date = {2018}, publisher = {{O'Reilly Media, Inc.}}, - file = {/home/riccardo/.local/share/zotero/files/zheng_casari_2018_feature_engineering_for_machine_learning.pdf} + url = {https://www.oreilly.com/library/view/feature-engineering-for/9781491953235}, + file = {/home/riccardo/.local/share/zotero/files/zheng_casari_2018_feature_engineering_for_machine_learning.pdf}, + isbn = {978-1-4919-5324-2} } @inproceedings{Zhu:2017:UnpairedImagetoimageTranslation, @@ -4051,9 +3167,12 @@ keywords = {⛔ No DOI found} } -@book{Zwiebach::FirstCourseString, +@book{Zwiebach:2009:FirstCourseString, title = {A {{First Course}} in {{String Theory}}}, author = {Zwiebach, Barton}, + date = {2009}, + publisher = {{Cambridge University Press}}, + url = {https://www.cambridge.org/academic/subjects/physics/theoretical-physics-and-mathematical-physics/first-course-string-theory-2nd-edition}, file = {/home/riccardo/.local/share/zotero/files/zwiebach_a_first_course_in_string_theory.pdf}, isbn = {978-0-521-88032-9}, langid = {english} diff --git a/thesis.cls b/thesis.cls index 662a0b4..aef85d5 100644 --- a/thesis.cls +++ b/thesis.cls @@ -201,7 +201,8 @@ \newenvironment{abstractpage} {% \thispagestyle{plain} - + \phantomsection + \addcontentsline{toc}{section}{Abstract} \noindent {\Large \sc Abstract} \\ \rule{0.99\linewidth}{\sepwidth} \\[2ex] } @@ -214,8 +215,9 @@ \newenvironment{acknowledgmentspage} {% \thispagestyle{plain} - - \noindent {\Large \sc Acknowledgements} \\ + \phantomsection + \addcontentsline{toc}{section}{Acknowledgements} + \noindent{\Large \sc Acknowledgements} \\ \rule{0.99\linewidth}{\sepwidth} \\[2ex] } {% @@ -238,6 +240,7 @@ \newcommand{\outline}[1] {% \thispagestyle{plain} + \phantomsection \section*{#1} \addcontentsline{toc}{section}{#1} } diff --git a/thesis.pdf b/thesis.pdf index dcb98f8d8badb2c0248a74dd54e34a601a4a9307..df5189c34815bfd68fc5203a58916f2f7270e560 100644 GIT binary patch delta 1152526 zcmb5UV~{UC6eZZUZTq!t+qP|6zjpU)8?SBKwr$(Cwf~u^-PzijFI$zmb#hbrkW_9? 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z?UA6GDhJ*mdxvofY#sP=cb>tKd5-m=l*@1CDK6ZDn96Dab?gZ`i>LqZ4ebBNB>$SD z_+h7G7Vx$5K&s z7|v!1ria`nEK54Cmt+?iH73>QVdVY!J$v`uFaK{(w@Z$&2I*qs>n~+phvY0W%Jlh| R2>6AC#qps~B^_n_{{_fVQ7Hfb diff --git a/thesis.tex b/thesis.tex index 5025309..9900909 100644 --- a/thesis.tex +++ b/thesis.tex @@ -14,6 +14,7 @@ \specialisation{Dottorato in Fisica ed Astrofisica} \logo{img/unito} +\renewcommand*{\bibfont}{\small} \addbibresource{thesis.bib} \fancyhead[L]{} diff --git a/tikz/complex_plane.pgf b/tikz/complex_plane.pgf index 7d51db9..67e8303 100644 --- a/tikz/complex_plane.pgf +++ b/tikz/complex_plane.pgf @@ -10,7 +10,7 @@ % draw arrows \draw[-latex] (0,0) -- (1.75cm, 1.75cm) node[anchor=south] (z1) {$\abs{z_{(1)}} = e^{\tau_{E\, (1)}}$}; -\draw[-latex] (0,0) -- (0.45cm, -0.9cm) node[anchor=north] (z0) {$\abs{z_{(0)}} = e^{\tau_{E\, (0)}}$}; +\draw[-latex] (0,0) -- (0.45cm, -0.9cm) node[anchor=north west] (z0) {$\abs{z_{(0)}} = e^{\tau_{E\, (0)}}$}; % draw isolated point \draw[fill] (-1.5cm, 1.1cm) circle (2pt) node[anchor=south west] (w) {$w$};

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