198 lines
6.8 KiB
TeX
198 lines
6.8 KiB
TeX
\documentclass[a4paper,11pt,twoside]{thesis}
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\usepackage[british]{babel}
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\usepackage{csquotes}
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\usepackage{debug}
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\usepackage{sciencestuff}
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\usepackage{import}
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\author{Riccardo Finotello}
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\title{D-branes and Deep Learning: \\ Theoretical and Computational Aspects In String Theory}
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\advisor{Igor Pesando}
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\institution{Università degli Studi di Torino}
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\school{Scuola di Dottorato}
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\specialisation{Dottorato in Fisica ed Astrofisica}
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\logo{img/unito}
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\renewcommand*{\bibfont}{\small}
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\addbibresource{thesis.bib}
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\fancyhead[L]{}
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\fancyhead[R]{\rightmark}
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\hypersetup{%
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pdftitle={D-branes and Deep Learning: Theoretical and Computational Aspects In String Theory},
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pdfauthor={Riccardo Finotello}
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}
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%---- abbreviations
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\newcommand{\ml}{\textsc{ml}\xspace}
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\newcommand{\fc}{\textsc{fc}\xspace}
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\newcommand{\eda}{\textsc{eda}\xspace}
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\newcommand{\pca}{\textsc{pca}\xspace}
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\newcommand{\svm}{\textsc{svm}\xspace}
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\newcommand{\bo}{\textsc{bo}\xspace}
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\newcommand{\nbo}{\textsc{nbo}\xspace}
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\newcommand{\gnbo}{\textsc{gnbo}\xspace}
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%---- functions
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\newcommand{\hyp}[4]{\ensuremath{\mathrm{F}\left( #1,\, #2;\, #3;\, #4 \right)}}
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\newcommand{\poch}[2]{\ensuremath{\left( #1 \right)_{#2}}}
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\newcommand{\gfun}[1]{\ensuremath{\Gamma\left( #1 \right)}}
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\newcommand{\hodge}[2]{\ensuremath{h^{#1,#2}}}
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%---- derivatives
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\newcommand{\consprod}[2]{\left\langle #1, #2 \right\rangle}
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\newcommand{\lconsprod}[2]{\left\langle\hspace{-0.25em}\left\langle #1\right.,\, #2 \right\rangle}
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\newcommand{\dual}[1]{\tensor[^*]{#1}{}}
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%---- integrals
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\newcommand{\ddz}{\ensuremath{\frac{\mathrm{d}z}{2 \pi i}}}
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\newcommand{\ddbz}{\ensuremath{\frac{\mathrm{d}\overline{z}}{2 \pi i}}}
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\newcommand{\ddw}{\ensuremath{\frac{\mathrm{d}w}{2 \pi i}}}
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\newcommand{\ddbw}{\ensuremath{\frac{\mathrm{d}\overline{w}}{2 \pi i}}}
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\newcommand{\cint}[1]{\ensuremath{\oint\limits_{\ccC_{#1}}}}
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%---- states
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\newcommand{\regvacuum}{\ensuremath{\ket{0}_{\SL{2}{R}}}\xspace}
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\newcommand{\regvacuumin}{\ensuremath{\ket{0_{(\text{in})}}_{\SL{2}{R}}}\xspace}
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\newcommand{\regvacuumout}{\ensuremath{\ket{0_{(\text{out})}}_{\SL{2}{R}}}\xspace}
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\newcommand{\regvacuuminconj}{\ensuremath{\tensor[_{\SL{2}{R}}]{\bra{0_{(\text{in})}}}{}}\xspace}
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\newcommand{\regvacuumoutconj}{\ensuremath{\tensor[_{\SL{2}{R}}]{\bra{0_{(\text{out})}}}{}}\xspace}
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\newcommand{\twsvacket}{\ensuremath{\ket{\mathrm{T}}}\xspace}
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\newcommand{\twsvacbra}{\ensuremath{\bra{\mathrm{T}}}\xspace}
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\newcommand{\excvacket}{\ensuremath{\ket{T_{\rE,\, \brE}}}\xspace}
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\newcommand{\excvacbra}{\ensuremath{\bra{T_{\rE,\, \brE}}}\xspace}
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\newcommand{\eexcvacket}{\ensuremath{\ket{T_{\rE}}}\xspace}
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\newcommand{\eexcvacbra}{\ensuremath{\bra{T_{\rE}}}\xspace}
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\newcommand{\Gexcvac}{\ensuremath{\Omega_{\qty{x_{(t)},\, \rE_{(t)},\, \brE_{(t)}}}}}
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\newcommand{\Gexcvacket}{\ensuremath{\ket{\Gexcvac}}}
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\newcommand{\Gexcvacbra}{\ensuremath{\bra{\Gexcvac}}}
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\newcommand{\GGexcvac}{\ensuremath{\Omega_{\qty{x_{(t)},\, \rE_{(t)}}}}}
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\newcommand{\GGexcvacket}{\ensuremath{\ket{\GGexcvac}}}
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\newcommand{\GGexcvacbra}{\ensuremath{\bra{\GGexcvac}}}
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\newcommand{\cmode}[4]{\ensuremath{\mathfrak{C}_{#1}\qty(#2,\, \qty{#4,\, #3})}}
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%---- operators
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\newcommand{\noE}[1]{\ccN_{\rE,\, \brE}\qty[ #1 ]}
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%---- coordinates
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\newcommand{\pX}{\ensuremath{X'}\xspace}
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\newcommand{\kmr}{\ensuremath{\qty{k_+,\, k_-,\, l,\, r}}}
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\newcommand{\kmkr}{\ensuremath{\qty{k_+,\, l,\, \vec{k},\, r}}}
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\newcommand{\kmkrN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, l_{\qty(#1)},\, \vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}}
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\newcommand{\kmrN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, k_{\qty(#1)\, -},\,l_{\qty(#1)},\, r_{\qty(#1)}}}}
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\newcommand{\mkmkr}{\ensuremath{\qty{-k_+,\, -l,\, -\vec{k},\, r}}}
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\newcommand{\mkmkrN}[1]{\ensuremath{\qty{-k_{\qty(#1)\, +},\, -l_{\qty(#1)},\, -\vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}}
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\newcommand{\kmkrgen}{\ensuremath{\qty{k_+,\, p,\, l,\, \vec{k},\, r}}}
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\newcommand{\kmkrgenN}[1]{\ensuremath{\qty{k_{\qty(#1)\, +},\, p_{\qty(#1)},\, l_{\qty(#1)},\, \vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}}
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\newcommand{\mkmkrgen}{\ensuremath{\qty{-k_+,\, -p,\, -l,\, -\vec{k},\, r}}}
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\newcommand{\mkmkrgenN}[1]{\ensuremath{\qty{-k_{\qty(#1)\, +},\, -p_{\qty(#1)},\, -l_{\qty(#1)},\, -\vec{k}_{\qty(#1)},\, r_{\qty(#1)}}}}
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\newcommand{\lkrsi}{\ensuremath{\qty{l,\, \vec{k},\, r,\, \sigma_-}}}
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\newcommand{\lsi}{\ensuremath{l\, \hsigma_-}}
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\newcommand{\lsiN}[1]{\ensuremath{l_{\qty(#1)}\, \hsigma_{-\, \qty(#1)}}}
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\newcommand{\pol}[1]{\ensuremath{\mathcal{E}_{\kmkr\, \underline{#1}}}}
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\newcommand{\polN}[2]{\ensuremath{\mathcal{E}_{\kmkrN{#2}\, \underline{#1}}}}
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\newcommand{\polabbrN}[2]{\ensuremath{\mathcal{E}_{\qty(#2)\, \underline{#1}}}}
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\newcommand{\genpolN}[1]{\ensuremath{\mathcal{E}_{\kmkrN{#1}}}}
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%---- BEGIN DOCUMENT
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\begin{document}
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%---- TITLE
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\maketitlepage{}
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\cleardoubleplainpage{}
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%---- FRONTESPICE
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\makefrontespice{}
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\cleardoubleplainpage{}
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%---- ABSTRACT
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\begin{abstractpage}
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\input{sec/abstract.tex}
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\end{abstractpage}
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\cleardoubleplainpage{}
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%---- ACKNOWLEDGENTS
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\begin{acknowledgmentspage}
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\input{sec/acknowledgments.tex}
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\end{acknowledgmentspage}
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\cleardoubleplainpage{}
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%---- TOC AND OUTLINE
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\plaintoc{}
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\outline{Outline}
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\input{sec/outline.tex}
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%---- PARTICLE PHYSICS
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\thesispart{Conformal Symmetry and Geometry of the Worldsheet}
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\label{part:cft}
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\section{Introduction}
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\input{sec/part1/introduction.tex}
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\section{D-branes Intersecting at Angles}
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\input{sec/part1/dbranes.tex}
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\section{Fermions With Boundary Defects}
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\input{sec/part1/fermions.tex}
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\section{Summary and Conclusion}
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\input{sec/part1/conclusion.tex}
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%---- COSMOLOGY
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\thesispart{Cosmological Backgrounds and Divergences}
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\label{part:cosmo}
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\section{Introduction}
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\input{sec/part2/introduction.tex}
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\section{Time Dependent Orbifolds}
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\input{sec/part2/divergences.tex}
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\section{Summary and Conclusion}
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\input{sec/part2/conclusion.tex}
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%---- DEEP LEARNING
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\thesispart{Deep Learning the Geometry of String Theory}
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\label{part:deeplearning}
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\section{Introduction}
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\input{sec/part3/introduction.tex}
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\section{Machine Learning and Deep Learning for CICY Manifolds}
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\input{sec/part3/ml.tex}
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\section{Summary and Conclusion}
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\label{sec:conclusion}
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\input{sec/part3/conclusion.tex}
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%---- APPENDIX
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\thesispart{Appendix}
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\label{part:appendix}
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\appendix
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\section{The Isomorphism in Details}
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\label{sec:isomorphism}
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\input{sec/app/isomorphism.tex}
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\section{The Parameters of the Hypergeometric Function}
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\label{sec:parameters}
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\input{sec/app/parameters.tex}
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\section{Reflection Conditions on the Vacuum}
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\label{sec:details_reflection}
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\input{sec/app/reflection.tex}
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\section{Tensor Wave Functions on NBO}
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\label{sec:NO_tensor_wave}
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\input{sec/app/tensor_wave.tex}
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\section{Overlap of Second Level Massive States on NBO}
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\label{sec:NO_full_TTS}
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\input{sec/app/massive.tex}
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\section{Machine Learning Algorithms}
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\label{app:ml-algo}
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\input{sec/app/ml.tex}
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%---- BIBLIOGRAPHY
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\cleardoubleplainpage{}
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\printbibliography[heading=bibintoc]
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\end{document}
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% vim: ft=tex
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