commit 77c0923a22ff01a291bb78dc31eff05419429309 Author: Riccardo Finotello Date: Tue Nov 3 18:41:57 2020 +0100 First commit with template Signed-off-by: Riccardo Finotello diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..b71074f --- /dev/null +++ b/.gitignore @@ -0,0 +1,12 @@ +img/*.xcf +*.aux +*.fdb_latexmk +*.fls +*.log +*.nav +*.out +*.snm +*.synctex.gz +*.thm +*.toc + diff --git a/img/complex_plane.pgf b/img/complex_plane.pgf new file mode 100644 index 0000000..fcc1325 --- /dev/null +++ b/img/complex_plane.pgf @@ -0,0 +1,25 @@ +\begin{tikzpicture} + +% draw axis +\draw[thick, ->] (-3cm, 0cm) -- (3cm, 0cm) node[anchor=south] {$\Re z$}; +\draw[thick, ->] (0cm, -3cm) -- (0cm, 3cm) node[anchor=east] {$\Im z$}; + +% draw closed loops +\draw[dotted, -latex] (1cm, 0cm) arc (0:360:1cm); +\draw[dotted, -latex] (2.5cm, 0cm) arc (0:360:2.5cm); + +% draw arrows +\draw[-latex] (0,0) -- (1.75cm, 1.75cm) node[anchor=south] (z1) {$\abs{z_{(1)}} = e^{\uptau_{E\, (1)}}$}; +\draw[-latex] (0,0) -- (0.45cm, -0.9cm) node[anchor=north west] (z0) {$\abs{z_{(0)}} = e^{\uptau_{E\, (0)}}$}; + +% draw isolated point +\draw[fill] (-1.5cm, 1.1cm) circle (2pt) node[anchor=south west] (w) {$w$}; + +% draw the names of the paths (use $\mathcal{C}$ instead of $\ccC$ if it does not compile) +\node (c0) at (-0.7cm, -1.2cm) {$\mathscr{C}_{(0)}$}; +\node (c0) at (-1.5cm, -2.6cm) {$\mathscr{C}_{(1)}$}; + +\end{tikzpicture} + + +% vim: ft=tex diff --git a/img/infn.pdf b/img/infn.pdf new file mode 100644 index 0000000..3c97980 Binary files /dev/null and b/img/infn.pdf differ diff --git a/img/torino.png b/img/torino.png new file mode 100644 index 0000000..c16f395 Binary files /dev/null and b/img/torino.png differ diff --git a/img/unito.pdf b/img/unito.pdf new file mode 100644 index 0000000..d9f14f5 Binary files /dev/null and b/img/unito.pdf differ diff --git a/thesis.tex b/thesis.tex new file mode 100644 index 0000000..986e452 --- /dev/null +++ b/thesis.tex @@ -0,0 +1,283 @@ +\documentclass[10pt, aspectratio=169]{beamer} + +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage[british]{babel} +\usepackage{csquotes} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{mathrsfs} +\usepackage{dsfont} +\usepackage{upgreek} +\usepackage{physics} +\usepackage{tensor} +\usepackage{graphicx} +\usepackage{transparent} +\usepackage{tikz} +\usepackage{import} +\usepackage{booktabs} +\usepackage{multicol} +\usepackage{multirow} +\usepackage{bookmark} +\usepackage{xspace} + +\usetheme{Singapore} +\usecolortheme{crane} +\usefonttheme{structurebold} +\setbeamertemplate{navigation symbols}{} + +\author[Finotello]{Riccardo Finotello} +\title[D-branes and Deep Learning]{D-branes and Deep Learning} +\subtitle{Theoretical and Computational Aspects in String Theory} +\institute[UniTO]{% + Scuola di Dottorato in Fisica e Astrofisica + \\[0.5em] + Università degli Studi di Torino + \\ + and + \\ + I.N.F.N.\ -- sezione di Torino +} +\date{15th December 2020} + +\newcommand{\firstlogo}{img/unito} +\newcommand{\thefirstlogo}{% + \begin{figure} + \centering + \includegraphics[width=5em]{\firstlogo} + \end{figure} +} + +\newcommand{\secondlogo}{img/infn} +\newcommand{\thesecondlogo}{% + \begin{figure} + \centering + \includegraphics[width=5em]{\secondlogo} + \end{figure} +} + +\setbeamertemplate{title page}{% + \begin{center} + {% + \usebeamercolor{title} + \usebeamerfont{title} + \colorbox{bg}{% + {\Huge \inserttitle}\xspace + } + \vspace{0.5em} + }\par + {% + \usebeamercolor{subtitle} + \usebeamerfont{subtitle} + {\large \it \insertsubtitle}\xspace + \vspace{2em} + }\par + {% + \usebeamercolor{author} + \usebeamerfont{author} + {\Large \insertauthor}\xspace + \vspace{1em} + }\par + {% + \begin{columns} + \centering + \begin{column}{0.3\linewidth} + \centering + \thefirstlogo + \end{column} + \begin{column}{0.4\linewidth} + \centering + \usebeamercolor{institute} + \usebeamerfont{institute} + \insertinstitute{} + \\[1em] + \insertdate{} + \end{column} + \begin{column}{0.3\linewidth} + \centering + \thesecondlogo + \end{column} + \end{columns} + }\par + \end{center} +} + +\setbeamertemplate{footline}{% + \usebeamerfont{footnote} + \usebeamercolor{footnote} + \hfill + \insertframenumber{}~/~\inserttotalframenumber{} + \hspace{1em} + \vspace{1em} + \par +} + +\AtBeginSection[] +{% + {% + \setbeamertemplate{footline}{} + \begin{frame}[noframenumbering]{\contentsname} + \tableofcontents[currentsection] + \end{frame} + } +} + + +\begin{document} + + {% + \usebackgroundtemplate{% + \transparent{0.1} + \includegraphics[width=\paperwidth]{img/torino.png} + } + \begin{frame}[noframenumbering, plain] + \titlepage{} + \end{frame} + } + + {% + \setbeamertemplate{footline}{} + \begin{frame}[noframenumbering]{\contentsname} + \tableofcontents{} + \end{frame} + } + + + \section[CFT]{Conformal Symmetry and Geometry of the Worldsheet} + + \begin{frame}{Action Principle and Conformal Symmetry} + \begin{block}{Polyakov's Action} + \begin{equation*} + S_P\qty[ \upgamma,\, X,\, \uppsi ] + = + -\frac{1}{4\pi} + \int\limits_{-\infty}^{+\infty} \dd{\uptau} + \int\limits_0^{\ell} \dd{\upsigma} + \sqrt{-\det \upgamma}\, + \upgamma^{\upalpha \upbeta}\, + \qty(% + \frac{2}{\alpha'}\, + \partial_{\upalpha} X^{\upmu}\, + \partial_{\upbeta} X^{\upnu} + + + \uppsi^{\upmu}\, + \uprho_{\upalpha} + \partial_{\upbeta} + \uppsi^{\upnu} + )\, + \upeta_{\upmu\upnu} + \end{equation*} + \end{block} + + \begin{columns} + \begin{column}[t]{0.5\linewidth} + Symmetries: + \begin{itemize} + \item Poincaré transf.\ $X'^{\upmu} = \tensor{\Uplambda}{^{\upmu}_{\upnu}} X^{\upnu} + c^{\upmu}$ + + \item 2D diff.\ $\upgamma'_{\upalpha \upbeta} = \tensor{\qty( \mathrm{J}^{-1} )}{_{\upalpha \upbeta}^{\uplambda \uprho}}\, \gamma_{\uplambda \uprho}$ + + \item Weyl transf.\ $\upgamma'_{\upalpha \upbeta} = e^{2 \upomega}\, \gamma_{\upalpha \upbeta}$ + \end{itemize} + \end{column} + + \begin{column}[t]{0.5\linewidth} + Conformal symmetry: + \begin{itemize} + \item vanishing stress-energy tensor: $\mathcal{T}_{\upalpha \upbeta} = 0$ + + \item traceless stress-energy tensor: $\trace{\mathcal{T}} = 0$ + + \item conformal gauge $\upgamma_{\upalpha \upbeta} = e^{\upphi}\, \upeta_{\upalpha \upbeta}$ + \end{itemize} + \end{column} + \end{columns} + \end{frame} + + \begin{frame}{Action Principle and Conformal Symmetry} + \begin{columns} + \begin{column}{0.6\linewidth} + Let $z = e^{\uptau_E + i \upsigma} \Rightarrow \overline{\partial} \mathcal{T}( z ) = \partial \overline{\mathcal{T}}( \overline{z} ) = 0$: + \begin{equation*} + T( z )\, \Upphi_{\upomega}( w ) + \stackrel{z \to w}{\sim} + \frac{\upomega}{(z - w)^2} \Upphi_{\upomega}( w ) + + + \frac{1}{z - w} \partial_w \Upphi_{\upomega}( w ) + \end{equation*} + \end{column} + + \begin{column}{0.4\linewidth} + \begin{figure}[h] + \centering + \resizebox{0.8\columnwidth}{!}{\import{img}{complex_plane.pgf}} + \end{figure} + \end{column} + \end{columns} + \end{frame} + + + \subsection[Tools]{Preliminary Tools and Definitions} + + \begin{frame}{AAA} + a1 + \end{frame} + + + \subsection[D-branes]{D-branes Intersecting at Angles} + + \begin{frame}{AAA} + a2 + \end{frame} + + + \subsection[Fermions]{Fermions With Boundary Defects} + + \begin{frame}{AAA} + a3 + \end{frame} + + + \section[Time Divergences]{Cosmological Backgrounds and Divergences} + + \begin{frame}{BBB} + b + \end{frame} + + + \subsection[Orbifolds]{Orbifolds and Cosmological Models} + + \begin{frame}{BBB} + b1 + \end{frame} + + + \subsection[Time Dependency]{Time Dependent Orbifolds} + + \begin{frame}{BBB} + b2 + \end{frame} + + + \section[Deep Learning]{Deep Learning the Geometry of String Theory} + + \begin{frame}{CCC} + c + \end{frame} + + \subsection[CICY]{Complete Intersection Calabi--Yau Manifolds} + + \begin{frame}{CCC} + c1 + \end{frame} + + + \subsection[Machine Learning]{Machine Learning and Deep Learning for CICY Manifolds} + + \begin{frame}{CCC} + c2 + \end{frame} + + +\end{document}