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\begin{document}

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\section*{type II string theory}

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

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

[[!include string theory - contents]]

\hypertarget{supergeometry}{}\paragraph*{{Super-Geometry}}\label{supergeometry}

[[!include supergeometry - contents]]

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

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{properties}{Properties}\dotfill \pageref*{properties} \linebreak
\noindent\hyperlink{effective_qft}{Effective QFT}\dotfill \pageref*{effective_qft} \linebreak
\noindent\hyperlink{anomaly_cancellation}{Anomaly cancellation}\dotfill \pageref*{anomaly_cancellation} \linebreak
\noindent\hyperlink{background_fields_and_orientifolding}{Background fields and orientifolding}\dotfill \pageref*{background_fields_and_orientifolding} \linebreak
\noindent\hyperlink{dualities}{Dualities}\dotfill \pageref*{dualities} \linebreak
\noindent\hyperlink{duality_with_heterotic_string_theory}{Duality with heterotic string theory}\dotfill \pageref*{duality_with_heterotic_string_theory} \linebreak
\noindent\hyperlink{duality_with_mtheory}{Duality with M-theory}\dotfill \pageref*{duality_with_mtheory} \linebreak
\noindent\hyperlink{duality_with_ftheory}{Duality with F-theory}\dotfill \pageref*{duality_with_ftheory} \linebreak
\noindent\hyperlink{holographic_dual}{Holographic dual}\dotfill \pageref*{holographic_dual} \linebreak
\noindent\hyperlink{partition_function_and_elliptic_genus}{Partition function and elliptic genus}\dotfill \pageref*{partition_function_and_elliptic_genus} \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{strings_and_sduality}{$(p,q)$-Strings and S-duality}\dotfill \pageref*{strings_and_sduality} \linebreak
\noindent\hyperlink{quantum_anomalies}{Quantum anomalies}\dotfill \pageref*{quantum_anomalies} \linebreak
\noindent\hyperlink{classical_solutions__vacua}{Classical solutions / vacua}\dotfill \pageref*{classical_solutions__vacua} \linebreak
\noindent\hyperlink{holography}{Holography}\dotfill \pageref*{holography} \linebreak


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

Perturbative [[string theory]] is defined in terms of certain classes of 2d [[CFT]]s. Depending on which class that is, one speaks of different \emph{types} of string theory.

\begin{itemize}%
\item In \emph{type II string theory} the CFTs in question are $(1,1)$-supersymmetric and defined on [[orientation|oriented]] [[worldsheet]]s;


\item In \emph{[[heterotic string theory]]} the CFTs in question are $(0,1)$-supersymmetric and defined on [[orientation|oriented]] [[worldsheet]]s;


\item In \ldots{}



\end{itemize}
\hypertarget{properties}{}\subsection*{{Properties}}\label{properties}

\hypertarget{effective_qft}{}\subsubsection*{{Effective QFT}}\label{effective_qft}

The [[effective quantum field theory]] of type II string theory containts --besides [[type II supergravity]] -- the [[self-dual higher gauge theory]] of [[RR-fields]] and [[Kalb-Ramond field]]s.

\hypertarget{anomaly_cancellation}{}\subsubsection*{{Anomaly cancellation}}\label{anomaly_cancellation}

Apart from the [[Weyl anomaly]], which cancels for 10-dimensional [[target space]]s, the [[action functional]] of the [[string]]-[[sigma-model]] also in general has an \emph{\href{http://ncatlab.org/nlab/show/quantum+anomaly#AnomalousActionFunctional}{anomalous action functional}} , for two reasons:

\begin{enumerate}%
\item The [[holonomy|higher holonomy]] of the higher [[background gauge field]]s is in general not a function, but a [[section]] of a [[line bundle]];


\item The fermionic [[path integral]] over the [[worldsheet]]-[[spinor]]s of the [[superstring]] produces as section of a [[Pfaffian line bundle]].



\end{enumerate}
In order for the action functional to be well-defined, the [[tensor product]] of these different anomaly [[line bundle]]s over the bosonic [[configuration space]] must have trivial class (as [[connection on a bundle|bundles with connection]], even). This gives rise to various further anomaly cancellation conditions:

For the open [[type II string]] the condition is known as the [[Freed-Witten anomaly cancellation]] condition: it says that the restriction of the [[B-field]] to any [[D-brane]] must consistute the twist of a [[twisted spin{\tt \symbol{94}}c structure]] on the brane.

A more detailed analysis of these type II anomalies is in (\hyperlink{DFMI}{DFMI}) and (\hyperlink{DFMII}{DFMII}).

\hypertarget{background_fields_and_orientifolding}{}\subsubsection*{{Background fields and orientifolding}}\label{background_fields_and_orientifolding}

[[!include string theory and cohomology theory -- table]]

\begin{itemize}%
\item [[intersecting D-brane models]]

\end{itemize}
\hypertarget{dualities}{}\subsubsection*{{Dualities}}\label{dualities}

Some [[dualities in string theory]] involving [[type II string theory]]:

\hypertarget{duality_with_heterotic_string_theory}{}\paragraph*{{Duality with heterotic string theory}}\label{duality_with_heterotic_string_theory}

See \emph{[[duality between type II and heterotic string theory]]}.

\hypertarget{duality_with_mtheory}{}\paragraph*{{Duality with M-theory}}\label{duality_with_mtheory}

See \emph{[[duality between type IIA string theory and M-theory]]}.

\hypertarget{duality_with_ftheory}{}\paragraph*{{Duality with F-theory}}\label{duality_with_ftheory}

See \emph{[[F-theory]]}.

\hypertarget{holographic_dual}{}\subsubsection*{{Holographic dual}}\label{holographic_dual}

By a [[holographic principle]] realized in this case as [[AdS/CFT correspondence]] (see the references there), type II string theory is supposed to be dual to 4-dimensional [[super Yang-Mills theory]].

\hypertarget{partition_function_and_elliptic_genus}{}\subsubsection*{{Partition function and elliptic genus}}\label{partition_function_and_elliptic_genus}

[[!include genera and partition functions - table]]

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

\begin{itemize}%
\item [[string theory]]

\begin{itemize}%
\item [[heterotic string theory]]

\begin{itemize}%
\item [[Green-Schwarz mechanism]]


\item [[dual heterotic string theory]]


\item [[Witten genus]], [[string orientation of tmf]]



\end{itemize}

\item \textbf{type II string theory}

[[Diaconescu-Moore-Witten anomaly]]

[[type II geometry]]

[[elliptic genus]]

4d [[super Yang-Mills theory]]


\item \textbf{[[type I string theory]]}


\item [[type 0 string theory]]



\end{itemize}

\item [[landscape of string theory vacua]]



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

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

Physics textbook accounts include

\begin{itemize}%
\item [[Joseph Polchinski]], \emph{[[String theory]]}, volume II, section 10


\item [[Eric D'Hoker]], \emph{String theory -- lecture 7: Free superstrings} , in part 3 of

[[Pierre Deligne]], [[Pavel Etingof]], [[Dan Freed]], L. Jeffrey, [[David Kazhdan]], [[John Morgan]], D.R. Morrison and [[Edward Witten]], eds. \emph{[[Quantum Fields and Strings]], A course for mathematicians}, 2 vols. Amer. Math. Soc. Providence 1999. (\href{http://www.math.ias.edu/qft}{web version})



\end{itemize}
A comprehensive discussion of the ([[differential cohomology|differential]]) [[cohomology|cohomological]] nature of general type II/type I [[orientifold]] backgrounds is in

\begin{itemize}%
\item [[Jacques Distler]], [[Dan Freed]], [[Greg Moore]], \emph{Orientifold Pr\'e{}cis} in: [[Hisham Sati]], [[Urs Schreiber]] (eds.) \emph{[[schreiber:Mathematical Foundations of Quantum Field and Perturbative String Theory]]} Proceedings of Symposia in Pure Mathematics, AMS (2011) (\href{http://arxiv.org/abs/0906.0795}{arXiv:0906.0795}, \href{http://www.ma.utexas.edu/users/dafr/bilbao.pdf}{slides})

\end{itemize}
with details in

\begin{itemize}%
\item [[Daniel Freed]], \emph{Lectures on twisted K-theory and orientifolds} ([[FreedESI2012.pdf:file]])


\item [[Jacques Distler]], [[Dan Freed]], [[Greg Moore]], \emph{Spin structures and superstrings}, Surveys in Differential Geometry, Volume 15 (2010) (\href{http://arxiv.org/abs/1007.4581}{arXiv:1007.4581}, \href{http://dx.doi.org/10.4310/SDG.2010.v15.n1.a4}{doi:10.4310/SDG.2010.v15.n1.a4})



\end{itemize}
Related lecture notes / slides include

\begin{itemize}%
\item [[Jacques Distler]], \emph{Orientifolds and Twisted KR-Theory} (2008) (\href{http://www.perimeterinstitute.ca/pdf/files/731c5f3a-928f-453a-b569-db5c574d2a6c.pdf}{pdf})


\item [[Daniel Freed]], \emph{Dirac charge quantiation, K-theory, and orientifolds}, talk at a workshop \emph{Mathematical methods in general relativity and quantum field theories}, November, 2009 (\href{http://www.ma.utexas.edu/users/dafr/paris_nt.pdf}{pdf})


\item [[Greg Moore]], \emph{The RR-charge of an orientifold} (\href{http://www.physics.rutgers.edu/~gmoore/AnnArbor_Feb2010_FINAL.ppt}{ppt})



\end{itemize}
\hypertarget{strings_and_sduality}{}\subsubsection*{{$(p,q)$-Strings and S-duality}}\label{strings_and_sduality}

\begin{itemize}%
\item [[John Schwarz]], opening talk at \href{http://strings2013.sogang.ac.kr/}{Strings 2013}, (\href{http://strings2013.sogang.ac.kr/design/default/data/john_schwarz.pdf}{pdf})

\end{itemize}
\hypertarget{quantum_anomalies}{}\subsubsection*{{Quantum anomalies}}\label{quantum_anomalies}

Discussion of type II [[quantum anomalies]] is in

\begin{itemize}%
\item [[Jacques Distler]], [[Dan Freed]], [[Greg Moore]], \emph{Orientifold Pr\'e{}cis} in: [[Hisham Sati]], [[Urs Schreiber]] (eds.) \emph{[[schreiber:Mathematical Foundations of Quantum Field and Perturbative String Theory]]} Proceedings of Symposia in Pure Mathematics, AMS (2011) (\href{http://arxiv.org/abs/0906.0795}{arXiv}, \href{http://www.ma.utexas.edu/users/dafr/bilbao.pdf}{slides})

\end{itemize}
\begin{itemize}%
\item [[Jacques Distler]], [[Dan Freed]], [[Greg Moore]], \emph{Spin structures and superstrings} (\href{http://arxiv.org/abs/1007.4581}{arXiv:1007.4581})

\end{itemize}
An exposition is at

\begin{itemize}%
\item [[Dan Freed]], \emph{Lectures on K-theory and orientifolds} (2012) (\href{http://www.ma.utexas.edu/users/dafr/ESI.pdf}{pdf})

\end{itemize}
\hypertarget{classical_solutions__vacua}{}\subsubsection*{{Classical solutions / vacua}}\label{classical_solutions__vacua}

Description of type II backgrounds in terms of [[generalized complex geometry]]/[[Courant Lie 2-algebroids]] is in

\begin{itemize}%
\item [[Mariana Grana]], Francesco Orsi, \emph{$N=1$ vacua in Exceptional Generalized Geometry} (\href{http://arxiv.org/abs/1105.4855}{arXiv:1105.4855})

\end{itemize}
\hypertarget{holography}{}\subsubsection*{{Holography}}\label{holography}

A [[holographic principle|holographic]] description of type II by [[higher dimensional Chern-Simons theory]] is discussed in

\begin{itemize}%
\item Dmitriy Belov, [[Greg Moore]], \emph{Type II Actions from 11-Dimensional Chern-Simons Theories} (\href{http://arxiv.org/abs/hep-th/0611020}{arXiv:hep-th/0611020})

\end{itemize}
[[!redirects type II superstring]] [[!redirects type II string]] [[!redirects type II superstrings]] [[!redirects type II strings]]

[[!redirects type II superstring theory]]

[[!redirects type IIA string theory]] [[!redirects type IIB string theory]] [[!redirects Type IIB string theory]]

[[!redirects type IIA superstring theory]] [[!redirects type IIB superstring theory]]

[[!redirects type IIA superstring]] [[!redirects type IIB superstring]] [[!redirects type IIA superstrings]] [[!redirects type IIB superstrings]]



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