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\begin{document}

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\section*{topological string}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{string_theory}{}\paragraph*{{String theory}}\label{string_theory}

[[!include string theory - contents]]

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{classification}{Classification}\dotfill \pageref*{classification} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{References}{References}\dotfill \pageref*{References} \linebreak
\noindent\hyperlink{general}{General}\dotfill \pageref*{general} \linebreak
\noindent\hyperlink{relation_to_black_hole_microstate_counting}{Relation to black hole microstate counting}\dotfill \pageref*{relation_to_black_hole_microstate_counting} \linebreak
\noindent\hyperlink{relation_to_physical_string_amplitudes}{Relation to physical string amplitudes}\dotfill \pageref*{relation_to_physical_string_amplitudes} \linebreak
\noindent\hyperlink{computation_via_topological_recursion}{Computation via topological recursion}\dotfill \pageref*{computation_via_topological_recursion} \linebreak


\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

In the broad sense of the word, a \emph{topological string} is a 2-dimensional [[TQFT]]. In its refined form this goes by the name \emph{[[TCFT]]}. The ``C'' standing for \emph{[[conformal field theory]]} points to what historically was the main inspiration and still is the default meaning of \emph{topological strings}: the \emph{[[A-model]]} and \emph{[[B-model]]} 2d TQFTs, which are each obtained by a ``topological twisting'' of [[2d SCFTs]].

Accordingly, much of ``physical'' [[string theory]] has its analogs in \emph{topological string theory}. Notably the toplogical analogs of the [[D-branes]] of the physical string -- the [[A-branes]] and [[B-branes]] -- have been studied in great (mathematical) detail, giving rise to [[homological mirror symmetry]] and, eventually, the notion of [[TCFT]] itself.

Also the perspective of [[string theory]] as the dimensional reduction of a conjectured [[UV-completion]] of [[11-dimensional supergravity]] -- ``M-theory'' -- has its analog for topological strings, going, accordingly, by the term \emph{[[topological M-theory]]}.

\hypertarget{classification}{}\subsection*{{Classification}}\label{classification}

[[!include 2d TQFT -- table]]

\hypertarget{related_concepts}{}\subsection*{{Related concepts}}\label{related_concepts}

\begin{itemize}%
\item [[TCFT]]

\begin{itemize}%
\item [[A-model]]
\item [[B-model]]

\end{itemize}

\item [[topological M-theory]], [[topological membrane]]



\end{itemize}
\hypertarget{References}{}\subsection*{{References}}\label{References}

\hypertarget{general}{}\subsubsection*{{General}}\label{general}

Review includes

\begin{itemize}%
\item [[Andrew Neitzke]], [[Cumrun Vafa]], \emph{Topological strings and their physical applications}, talk at \href{http://insti.physics.sunysb.edu/conf/simonsworkII/}{Simons Workshop in Mathematics and Physics 2004} (\href{http://xxx.lanl.gov/abs/hep-th/0410178}{hep-th/0410178})


\item I. Antoniadis, S. Hohenegger, \emph{Topological Amplitudes and Physical Couplings in String Theory}, Nucl.Phys.Proc.Suppl.171:176-195,2007 (\href{https://arxiv.org/abs/hep-th/0701290}{arXiv:hep-th/0701290})


\item Marcel Vonk, \emph{A mini-course on topological strings} (\href{http://arxiv.org/abs/hep-th/0504147}{arXiv:hep-th/0504147})


\item [[Andrew Neitzke]], \emph{Nonperturbative topological strings}, 2005 (\href{http://people.maths.ox.ac.uk/lmason/Tws/Neitzke.pdf}{pdf})



\end{itemize}
The relation to [[topological M-theory]]/the [[topological membrane]] is discussed for instance in

\begin{itemize}%
\item [[Jan de Boer]], Paul de Medeiros, Sheer El-Showk, Annamaria Sinkovics, \emph{Open $G_2$ Strings} (\href{http://arxiv.org/abs/hep-th/0611080}{arXiv:hep-th/0611080})

\end{itemize}
See also

\begin{itemize}%
\item wikipedia \href{http://en.wikipedia.org/wiki/Topological_string_theory}{topological string theory}


\item Lotte Hollands, \emph{Topological Strings and Quantum Curves} (\href{https://arxiv.org/abs/0911.3413}{arXiv:0911.3413})


\item Mina Aganagi, [[Cumrun Vafa]], \emph{Large N duality, mirror symmetry, and a Q-deformed A-polynomial for knots}, \href{http://arxiv.org/abs/1204.4709}{arxiv/1204.4709}


\item Min-xin Huang, \emph{Recent Developments in Topological String Theory} (\href{https://arxiv.org/abs/1812.03636}{arXiv:1812.03636})



\end{itemize}
\hypertarget{relation_to_black_hole_microstate_counting}{}\subsubsection*{{Relation to black hole microstate counting}}\label{relation_to_black_hole_microstate_counting}

Disucssion of [[black holes in string theory]] via the topological string' [[Gopakumar-Vafa invariants]]:

\begin{itemize}%
\item [[Rajesh Gopakumar]], [[Cumrun Vafa]], \emph{M-Theory and Topological Strings--I} (\href{https://arxiv.org/abs/hep-th/9809187}{arXiv:hep-th/9809187})


\item [[Rajesh Gopakumar]], [[Cumrun Vafa]], \emph{M-Theory and Topological Strings--II} (\href{https://arxiv.org/abs/hep-th/9812127}{arXiv:hep-th/9812127})



\end{itemize}
\hypertarget{relation_to_physical_string_amplitudes}{}\subsubsection*{{Relation to physical string amplitudes}}\label{relation_to_physical_string_amplitudes}

The following includes discussion of [[superstring]] [[string scattering amplitudes]] in terms of topological string scattering amplitudes (for review see \hyperlink{NeitzkeVafa04}{NeitzkeVafa04, section 6} and \hyperlink{AntoniadisHohenegger07}{Antoniadis-Hohenegger 07}:

\begin{itemize}%
\item M. Bershadsky, S. Cecotti, [[Hirosi Ooguri]], [[Cumrun Vafa]], \emph{Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes}, Commun.Math.Phys.165:311-428,1994 (\href{https://arxiv.org/abs/hep-th/9309140}{arXiv:hep-th/9309140})


\item I. Antoniadis, E. Gava, K.S. Narain, T.R. Taylor, \emph{Topological Amplitudes in String Theory}, Nucl.Phys. B413 (1994) 162-184 (\href{http://xxx.lanl.gov/abs/hep-th/9307158}{arXiv:hep-th/9307158})


\item K.S. Narain, N. Piazzalunga, A. Tanzini, \emph{Real topological string amplitudes}, JHEP (2017) 2017:80 (\href{https://arxiv.org/abs/1612.07544}{arXiv:1612.07544})



\end{itemize}
\hypertarget{computation_via_topological_recursion}{}\subsubsection*{{Computation via topological recursion}}\label{computation_via_topological_recursion}

Computation via [[topological recursion]] in [[matrix models]] and all-[[genus of a surface|genus]] proofs of [[mirror symmetry]] is due to

\begin{itemize}%
\item [[Vincent Bouchard]], [[Albrecht Klemm]], [[Marcos Marino]], [[Sara Pasquetti]], \emph{Remodeling the B-model}, Commun.Math.Phys.287:117-178, 2009 (\href{https://arxiv.org/abs/0709.1453}{arXiv:0709.1453})


\item [[Bertrand Eynard]], [[Amir-Kian Kashani-Poor]], Olivier Marchal, \emph{A matrix model for the topological string I: Deriving the matrix model} (\href{https://arxiv.org/abs/1003.1737}{arXiv:1003.1737})


\item [[Bertrand Eynard]], [[Amir-Kian Kashani-Poor]], Olivier Marchal, \emph{A matrix model for the topological string II: The spectral curve and mirror geometry} (\href{https://arxiv.org/abs/1007.2194}{arXiv:1007.2194})


\item [[Bertrand Eynard]], [[Nicolas Orantin]], \emph{Computation of open Gromov-Witten invariants for toric Calabi-Yau 3-folds by topological recursion, a proof of the BKMP conjecture} (\href{https://arxiv.org/abs/1205.1103}{arXiv:1205.1103})


\item Bohan Fang, Chiu-Chu Melissa Liu, Zhengyu Zong, \emph{All Genus Open-Closed Mirror Symmetry for Affine Toric Calabi-Yau 3-Orbifolds} (\href{https://arxiv.org/abs/1310.4818}{arXiv:1310.4818})



\end{itemize}
[[!redirects topological strings]]

[[!redirects topological string theory]]



\end{document}