\documentclass[12pt,titlepage]{article} \usepackage{amsmath} \usepackage{mathrsfs} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsthm} \usepackage{mathtools} \usepackage{graphicx} \usepackage{color} \usepackage{ucs} \usepackage[utf8x]{inputenc} \usepackage{xparse} \usepackage{hyperref} %----Macros---------- % % Unresolved issues: % % \righttoleftarrow % \lefttorightarrow % % \color{} with HTML colorspec % \bgcolor % \array with options (without options, it's equivalent to the matrix environment) % Of the standard HTML named colors, white, black, red, green, blue and yellow % are predefined in the color package. Here are the rest. \definecolor{aqua}{rgb}{0, 1.0, 1.0} \definecolor{fuschia}{rgb}{1.0, 0, 1.0} \definecolor{gray}{rgb}{0.502, 0.502, 0.502} \definecolor{lime}{rgb}{0, 1.0, 0} \definecolor{maroon}{rgb}{0.502, 0, 0} \definecolor{navy}{rgb}{0, 0, 0.502} \definecolor{olive}{rgb}{0.502, 0.502, 0} \definecolor{purple}{rgb}{0.502, 0, 0.502} \definecolor{silver}{rgb}{0.753, 0.753, 0.753} \definecolor{teal}{rgb}{0, 0.502, 0.502} % Because of conflicts, \space and \mathop are converted to % \itexspace and \operatorname during preprocessing. % itex: \space{ht}{dp}{wd} % % Height and baseline depth measurements are in units of tenths of an ex while % the width is measured in tenths of an em. \makeatletter \newdimen\itex@wd% \newdimen\itex@dp% \newdimen\itex@thd% \def\itexspace#1#2#3{\itex@wd=#3em% \itex@wd=0.1\itex@wd% \itex@dp=#2ex% \itex@dp=0.1\itex@dp% \itex@thd=#1ex% \itex@thd=0.1\itex@thd% \advance\itex@thd\the\itex@dp% \makebox[\the\itex@wd]{\rule[-\the\itex@dp]{0cm}{\the\itex@thd}}} \makeatother % \tensor and \multiscript \makeatletter \newif\if@sup \newtoks\@sups \def\append@sup#1{\edef\act{\noexpand\@sups={\the\@sups #1}}\act}% \def\reset@sup{\@supfalse\@sups={}}% \def\mk@scripts#1#2{\if #2/ \if@sup ^{\the\@sups}\fi \else% \ifx #1_ \if@sup ^{\the\@sups}\reset@sup \fi {}_{#2}% \else \append@sup#2 \@suptrue \fi% \expandafter\mk@scripts\fi} \def\tensor#1#2{\reset@sup#1\mk@scripts#2_/} \def\multiscripts#1#2#3{\reset@sup{}\mk@scripts#1_/#2% \reset@sup\mk@scripts#3_/} \makeatother % \slash \makeatletter \newbox\slashbox \setbox\slashbox=\hbox{$/$} \def\itex@pslash#1{\setbox\@tempboxa=\hbox{$#1$} \@tempdima=0.5\wd\slashbox \advance\@tempdima 0.5\wd\@tempboxa \copy\slashbox \kern-\@tempdima \box\@tempboxa} \def\slash{\protect\itex@pslash} \makeatother % math-mode versions of \rlap, etc % from Alexander Perlis, "A complement to \smash, \llap, and lap" % http://math.arizona.edu/~aprl/publications/mathclap/ \def\clap#1{\hbox to 0pt{\hss#1\hss}} \def\mathllap{\mathpalette\mathllapinternal} \def\mathrlap{\mathpalette\mathrlapinternal} \def\mathclap{\mathpalette\mathclapinternal} \def\mathllapinternal#1#2{\llap{$\mathsurround=0pt#1{#2}$}} \def\mathrlapinternal#1#2{\rlap{$\mathsurround=0pt#1{#2}$}} \def\mathclapinternal#1#2{\clap{$\mathsurround=0pt#1{#2}$}} % Renames \sqrt as \oldsqrt and redefine root to result in \sqrt[#1]{#2} \let\oldroot\root \def\root#1#2{\oldroot #1 \of{#2}} \renewcommand{\sqrt}[2][]{\oldroot #1 \of{#2}} % Manually declare the txfonts symbolsC font \DeclareSymbolFont{symbolsC}{U}{txsyc}{m}{n} \SetSymbolFont{symbolsC}{bold}{U}{txsyc}{bx}{n} \DeclareFontSubstitution{U}{txsyc}{m}{n} % Manually declare the stmaryrd font \DeclareSymbolFont{stmry}{U}{stmry}{m}{n} \SetSymbolFont{stmry}{bold}{U}{stmry}{b}{n} % Manually declare the MnSymbolE font \DeclareFontFamily{OMX}{MnSymbolE}{} \DeclareSymbolFont{mnomx}{OMX}{MnSymbolE}{m}{n} \SetSymbolFont{mnomx}{bold}{OMX}{MnSymbolE}{b}{n} \DeclareFontShape{OMX}{MnSymbolE}{m}{n}{ <-6> MnSymbolE5 <6-7> MnSymbolE6 <7-8> MnSymbolE7 <8-9> MnSymbolE8 <9-10> MnSymbolE9 <10-12> MnSymbolE10 <12-> MnSymbolE12}{} % Declare specific arrows from txfonts without loading the full package \makeatletter \def\re@DeclareMathSymbol#1#2#3#4{% \let#1=\undefined \DeclareMathSymbol{#1}{#2}{#3}{#4}} \re@DeclareMathSymbol{\neArrow}{\mathrel}{symbolsC}{116} \re@DeclareMathSymbol{\neArr}{\mathrel}{symbolsC}{116} \re@DeclareMathSymbol{\seArrow}{\mathrel}{symbolsC}{117} \re@DeclareMathSymbol{\seArr}{\mathrel}{symbolsC}{117} \re@DeclareMathSymbol{\nwArrow}{\mathrel}{symbolsC}{118} \re@DeclareMathSymbol{\nwArr}{\mathrel}{symbolsC}{118} \re@DeclareMathSymbol{\swArrow}{\mathrel}{symbolsC}{119} \re@DeclareMathSymbol{\swArr}{\mathrel}{symbolsC}{119} \re@DeclareMathSymbol{\nequiv}{\mathrel}{symbolsC}{46} \re@DeclareMathSymbol{\Perp}{\mathrel}{symbolsC}{121} \re@DeclareMathSymbol{\Vbar}{\mathrel}{symbolsC}{121} \re@DeclareMathSymbol{\sslash}{\mathrel}{stmry}{12} \re@DeclareMathSymbol{\bigsqcap}{\mathop}{stmry}{"64} \re@DeclareMathSymbol{\biginterleave}{\mathop}{stmry}{"6} \re@DeclareMathSymbol{\invamp}{\mathrel}{symbolsC}{77} \re@DeclareMathSymbol{\parr}{\mathrel}{symbolsC}{77} \makeatother % \llangle, \rrangle, \lmoustache and \rmoustache from MnSymbolE \makeatletter \def\Decl@Mn@Delim#1#2#3#4{% \if\relax\noexpand#1% \let#1\undefined \fi \DeclareMathDelimiter{#1}{#2}{#3}{#4}{#3}{#4}} \def\Decl@Mn@Open#1#2#3{\Decl@Mn@Delim{#1}{\mathopen}{#2}{#3}} \def\Decl@Mn@Close#1#2#3{\Decl@Mn@Delim{#1}{\mathclose}{#2}{#3}} \Decl@Mn@Open{\llangle}{mnomx}{'164} \Decl@Mn@Close{\rrangle}{mnomx}{'171} \Decl@Mn@Open{\lmoustache}{mnomx}{'245} \Decl@Mn@Close{\rmoustache}{mnomx}{'244} \makeatother % Widecheck \makeatletter \DeclareRobustCommand\widecheck[1]{{\mathpalette\@widecheck{#1}}} \def\@widecheck#1#2{% \setbox\z@\hbox{\m@th$#1#2$}% \setbox\tw@\hbox{\m@th$#1% \widehat{% \vrule\@width\z@\@height\ht\z@ \vrule\@height\z@\@width\wd\z@}$}% \dp\tw@-\ht\z@ \@tempdima\ht\z@ \advance\@tempdima2\ht\tw@ \divide\@tempdima\thr@@ \setbox\tw@\hbox{% \raise\@tempdima\hbox{\scalebox{1}[-1]{\lower\@tempdima\box \tw@}}}% {\ooalign{\box\tw@ \cr \box\z@}}} \makeatother % \mathraisebox{voffset}[height][depth]{something} \makeatletter \NewDocumentCommand\mathraisebox{moom}{% \IfNoValueTF{#2}{\def\@temp##1##2{\raisebox{#1}{$\m@th##1##2$}}}{% \IfNoValueTF{#3}{\def\@temp##1##2{\raisebox{#1}[#2]{$\m@th##1##2$}}% }{\def\@temp##1##2{\raisebox{#1}[#2][#3]{$\m@th##1##2$}}}}% \mathpalette\@temp{#4}} \makeatletter % udots (taken from yhmath) \makeatletter \def\udots{\mathinner{\mkern2mu\raise\p@\hbox{.} \mkern2mu\raise4\p@\hbox{.}\mkern1mu \raise7\p@\vbox{\kern7\p@\hbox{.}}\mkern1mu}} \makeatother %% Fix array \newcommand{\itexarray}[1]{\begin{matrix}#1\end{matrix}} %% \itexnum is a noop \newcommand{\itexnum}[1]{#1} %% Renaming existing commands \newcommand{\underoverset}[3]{\underset{#1}{\overset{#2}{#3}}} \newcommand{\widevec}{\overrightarrow} \newcommand{\darr}{\downarrow} \newcommand{\nearr}{\nearrow} \newcommand{\nwarr}{\nwarrow} \newcommand{\searr}{\searrow} \newcommand{\swarr}{\swarrow} \newcommand{\curvearrowbotright}{\curvearrowright} \newcommand{\uparr}{\uparrow} \newcommand{\downuparrow}{\updownarrow} \newcommand{\duparr}{\updownarrow} \newcommand{\updarr}{\updownarrow} \newcommand{\gt}{>} \newcommand{\lt}{<} \newcommand{\map}{\mapsto} \newcommand{\embedsin}{\hookrightarrow} \newcommand{\Alpha}{A} \newcommand{\Beta}{B} \newcommand{\Zeta}{Z} \newcommand{\Eta}{H} \newcommand{\Iota}{I} \newcommand{\Kappa}{K} \newcommand{\Mu}{M} \newcommand{\Nu}{N} \newcommand{\Rho}{P} \newcommand{\Tau}{T} \newcommand{\Upsi}{\Upsilon} \newcommand{\omicron}{o} \newcommand{\lang}{\langle} \newcommand{\rang}{\rangle} \newcommand{\Union}{\bigcup} \newcommand{\Intersection}{\bigcap} \newcommand{\Oplus}{\bigoplus} \newcommand{\Otimes}{\bigotimes} \newcommand{\Wedge}{\bigwedge} \newcommand{\Vee}{\bigvee} \newcommand{\coproduct}{\coprod} \newcommand{\product}{\prod} \newcommand{\closure}{\overline} \newcommand{\integral}{\int} \newcommand{\doubleintegral}{\iint} \newcommand{\tripleintegral}{\iiint} \newcommand{\quadrupleintegral}{\iiiint} \newcommand{\conint}{\oint} \newcommand{\contourintegral}{\oint} \newcommand{\infinity}{\infty} \newcommand{\bottom}{\bot} \newcommand{\minusb}{\boxminus} \newcommand{\plusb}{\boxplus} \newcommand{\timesb}{\boxtimes} \newcommand{\intersection}{\cap} \newcommand{\union}{\cup} \newcommand{\Del}{\nabla} \newcommand{\odash}{\circleddash} \newcommand{\negspace}{\!} \newcommand{\widebar}{\overline} \newcommand{\textsize}{\normalsize} \renewcommand{\scriptsize}{\scriptstyle} \newcommand{\scriptscriptsize}{\scriptscriptstyle} \newcommand{\mathfr}{\mathfrak} \newcommand{\statusline}[2]{#2} \newcommand{\tooltip}[2]{#2} \newcommand{\toggle}[2]{#2} % Theorem Environments \theoremstyle{plain} \newtheorem{theorem}{Theorem} \newtheorem{lemma}{Lemma} \newtheorem{prop}{Proposition} \newtheorem{cor}{Corollary} \newtheorem*{utheorem}{Theorem} \newtheorem*{ulemma}{Lemma} \newtheorem*{uprop}{Proposition} \newtheorem*{ucor}{Corollary} \theoremstyle{definition} \newtheorem{defn}{Definition} \newtheorem{example}{Example} \newtheorem*{udefn}{Definition} \newtheorem*{uexample}{Example} \theoremstyle{remark} \newtheorem{remark}{Remark} \newtheorem{note}{Note} \newtheorem*{uremark}{Remark} \newtheorem*{unote}{Note} %------------------------------------------------------------------- \begin{document} %------------------------------------------------------------------- \section*{String theory} \hypertarget{context}{}\subsubsection*{{Context}}\label{context} \hypertarget{string_theory}{}\paragraph*{{String theory}}\label{string_theory} [[!include string theory - contents]] \hypertarget{physics}{}\paragraph*{{Physics}}\label{physics} [[!include physicscontents]] This entry collects links related to the textbook \begin{itemize}% \item [[Joseph Polchinski]], \emph{String theory} Cambridge Monographs on Mathematical Physics first published 1998 \end{itemize} on [[string theory]]. \begin{itemize}% \item Volume 1: An introduction to the bosonic string (\href{http://stringworld.ru/files/Polchinski_J._String_theory._Vol._1._An_introduction_to_the_bosonic_string.pdf}{pdf}) \end{itemize} on [[bosonic string theory]] \begin{itemize}% \item Volume 2: Superstring theory and beyond (\href{http://stringworld.ru/files/Polchinski_J._String_theory._Vol._2._Superstring_theory_and_beyond.pdf}{pdf}) \end{itemize} on [[superstring theory]] and [[M-theory]]. See also at \emph{[[string theory FAQ]]} $\backslash$linebreak \hypertarget{contents}{}\section*{{Contents}}\label{contents} \noindent\hyperlink{volume_1_an_introduction_to_the_bosonic_string}{Volume 1 An introduction to the bosonic string}\dotfill \pageref*{volume_1_an_introduction_to_the_bosonic_string} \linebreak \noindent\hyperlink{1_a_first_look_at_strings}{1 A first look at strings}\dotfill \pageref*{1_a_first_look_at_strings} \linebreak \noindent\hyperlink{2_conformal_field_theory}{2 Conformal field theory}\dotfill \pageref*{2_conformal_field_theory} \linebreak \noindent\hyperlink{3_the_polyakov_path_integral}{3 The Polyakov path integral}\dotfill \pageref*{3_the_polyakov_path_integral} \linebreak \noindent\hyperlink{4_the_string_spectrum}{4 The string spectrum}\dotfill \pageref*{4_the_string_spectrum} \linebreak \noindent\hyperlink{5_the_string_smatrix}{5 The string S-matrix}\dotfill \pageref*{5_the_string_smatrix} \linebreak \noindent\hyperlink{6_treeleve_amplitudes}{6 Tree-leve amplitudes}\dotfill \pageref*{6_treeleve_amplitudes} \linebreak \noindent\hyperlink{6_oneloop_amplitudes}{6 One-loop amplitudes}\dotfill \pageref*{6_oneloop_amplitudes} \linebreak \noindent\hyperlink{7_toroidal_compatifications_and_tduality}{7 Toroidal compatifications and T-duality}\dotfill \pageref*{7_toroidal_compatifications_and_tduality} \linebreak \noindent\hyperlink{8_higher_order_amplitudes}{8 Higher order amplitudes}\dotfill \pageref*{8_higher_order_amplitudes} \linebreak \noindent\hyperlink{appenix_a_a_short_course_on_path_integrals}{Appenix A: A short course on path integrals}\dotfill \pageref*{appenix_a_a_short_course_on_path_integrals} \linebreak \noindent\hyperlink{volume_2_superstring_theory_and_beyond}{Volume 2 Superstring theory and beyond}\dotfill \pageref*{volume_2_superstring_theory_and_beyond} \linebreak \noindent\hyperlink{10_type_i_and_type_ii_superstrings}{10 Type I and type II superstrings}\dotfill \pageref*{10_type_i_and_type_ii_superstrings} \linebreak \noindent\hyperlink{11_the_heterotic_string}{11 The heterotic string}\dotfill \pageref*{11_the_heterotic_string} \linebreak \noindent\hyperlink{12_superstring_interaction}{12 Superstring interaction}\dotfill \pageref*{12_superstring_interaction} \linebreak \noindent\hyperlink{13_dbranes}{13 D-Branes}\dotfill \pageref*{13_dbranes} \linebreak \noindent\hyperlink{14_strings_at_strong_coupling}{14 Strings at strong coupling}\dotfill \pageref*{14_strings_at_strong_coupling} \linebreak \noindent\hyperlink{15_advanced_cft}{15 Advanced CFT}\dotfill \pageref*{15_advanced_cft} \linebreak \noindent\hyperlink{16_orbifold}{16 Orbifold}\dotfill \pageref*{16_orbifold} \linebreak \noindent\hyperlink{17_calabiyau_compactifictions}{17 Calabi-Yau compactifictions}\dotfill \pageref*{17_calabiyau_compactifictions} \linebreak \noindent\hyperlink{18_physics_in_four_dimensions}{18 Physics in four dimensions}\dotfill \pageref*{18_physics_in_four_dimensions} \linebreak \noindent\hyperlink{19_advanced_topics}{19 Advanced topics}\dotfill \pageref*{19_advanced_topics} \linebreak \noindent\hyperlink{appendix_b_spinors_and_susy_in_various_dimensions}{Appendix B: Spinors and SUSY in various dimensions}\dotfill \pageref*{appendix_b_spinors_and_susy_in_various_dimensions} \linebreak \hypertarget{volume_1_an_introduction_to_the_bosonic_string}{}\subsection*{{Volume 1 An introduction to the bosonic string}}\label{volume_1_an_introduction_to_the_bosonic_string} \hypertarget{1_a_first_look_at_strings}{}\subsubsection*{{1 A first look at strings}}\label{1_a_first_look_at_strings} \begin{itemize}% \item [[sigma model]] \item [[string]] \end{itemize} \hypertarget{2_conformal_field_theory}{}\subsubsection*{{2 Conformal field theory}}\label{2_conformal_field_theory} \begin{itemize}% \item [[2d CFT]] \end{itemize} \hypertarget{3_the_polyakov_path_integral}{}\subsubsection*{{3 The Polyakov path integral}}\label{3_the_polyakov_path_integral} \begin{itemize}% \item [[Polyakov action]] \item [[path integral]] \end{itemize} \hypertarget{4_the_string_spectrum}{}\subsubsection*{{4 The string spectrum}}\label{4_the_string_spectrum} \begin{itemize}% \item [[BRST-BV formalism]] \end{itemize} \hypertarget{5_the_string_smatrix}{}\subsubsection*{{5 The string S-matrix}}\label{5_the_string_smatrix} \begin{itemize}% \item [[S-matrix]] \item [[string scattering amplitude]] \end{itemize} \hypertarget{6_treeleve_amplitudes}{}\subsubsection*{{6 Tree-leve amplitudes}}\label{6_treeleve_amplitudes} \begin{itemize}% \item [[string scattering amplitude]] \end{itemize} \hypertarget{6_oneloop_amplitudes}{}\subsubsection*{{6 One-loop amplitudes}}\label{6_oneloop_amplitudes} \begin{itemize}% \item [[string scattering amplitude]] \end{itemize} \hypertarget{7_toroidal_compatifications_and_tduality}{}\subsubsection*{{7 Toroidal compatifications and T-duality}}\label{7_toroidal_compatifications_and_tduality} \begin{itemize}% \item [[KK-compactification]] \item [[T-duality]] \end{itemize} \hypertarget{8_higher_order_amplitudes}{}\subsubsection*{{8 Higher order amplitudes}}\label{8_higher_order_amplitudes} \begin{itemize}% \item [[string scattering amplitudes]] \end{itemize} \hypertarget{appenix_a_a_short_course_on_path_integrals}{}\subsubsection*{{Appenix A: A short course on path integrals}}\label{appenix_a_a_short_course_on_path_integrals} \begin{itemize}% \item [[path integral]] \end{itemize} \hypertarget{volume_2_superstring_theory_and_beyond}{}\subsection*{{Volume 2 Superstring theory and beyond}}\label{volume_2_superstring_theory_and_beyond} \hypertarget{10_type_i_and_type_ii_superstrings}{}\subsubsection*{{10 Type I and type II superstrings}}\label{10_type_i_and_type_ii_superstrings} \begin{itemize}% \item [[type II string theory]] \item [[type I string theory]] \end{itemize} \hypertarget{11_the_heterotic_string}{}\subsubsection*{{11 The heterotic string}}\label{11_the_heterotic_string} \begin{itemize}% \item [[heterotic string theory]] \end{itemize} \hypertarget{12_superstring_interaction}{}\subsubsection*{{12 Superstring interaction}}\label{12_superstring_interaction} (\ldots{}) \hypertarget{13_dbranes}{}\subsubsection*{{13 D-Branes}}\label{13_dbranes} \begin{itemize}% \item [[D-brane]] \end{itemize} \hypertarget{14_strings_at_strong_coupling}{}\subsubsection*{{14 Strings at strong coupling}}\label{14_strings_at_strong_coupling} \begin{itemize}% \item [[non-perturbative field theory]] \item [[11-dimensional supergravity]] \item [[M-theory]] \end{itemize} \hypertarget{15_advanced_cft}{}\subsubsection*{{15 Advanced CFT}}\label{15_advanced_cft} \begin{itemize}% \item [[CFT]] \end{itemize} \hypertarget{16_orbifold}{}\subsubsection*{{16 Orbifold}}\label{16_orbifold} \begin{itemize}% \item [[orbifold]] \end{itemize} \hypertarget{17_calabiyau_compactifictions}{}\subsubsection*{{17 Calabi-Yau compactifictions}}\label{17_calabiyau_compactifictions} \begin{itemize}% \item [[Calabi-Yau manifold]] \item [[KK-compactification]] \item [[landscape of string theory vacua]] \end{itemize} \hypertarget{18_physics_in_four_dimensions}{}\subsubsection*{{18 Physics in four dimensions}}\label{18_physics_in_four_dimensions} \begin{itemize}% \item [[effective field theory]] \item [[string phenomenology]] \end{itemize} \hypertarget{19_advanced_topics}{}\subsubsection*{{19 Advanced topics}}\label{19_advanced_topics} \begin{itemize}% \item [[mirror symmetry]] \item [[S-duality]] \end{itemize} \hypertarget{appendix_b_spinors_and_susy_in_various_dimensions}{}\subsubsection*{{Appendix B: Spinors and SUSY in various dimensions}}\label{appendix_b_spinors_and_susy_in_various_dimensions} \begin{itemize}% \item [[spinor]], [[spin representation]], \item [[super Poincare Lie algebra]] \item [[supersymmetry]] \end{itemize} category: reference \end{document}