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\begin{document}

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\section*{Poisson-Lie T-duality}

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

\hypertarget{duality_in_string_theory}{}\paragraph*{{Duality in string theory}}\label{duality_in_string_theory}

[[!include duality in string theory -- contents]]

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

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{as_a_partial_duality_of_string_theory}{As a partial duality of string theory}\dotfill \pageref*{as_a_partial_duality_of_string_theory} \linebreak
\noindent\hyperlink{related_lab_entries}{Related $n$Lab entries}\dotfill \pageref*{related_lab_entries} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak


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

What has come to be called \emph{nonabelian T-duality} (\hyperlink{OssaQuevedo92}{Ossa-Quevedo 92}) \emph{Poisson-Lie T-Duality} (due to \hyperlink{KlimcikSevera95}{Klimcik-Ševera 95}, \hyperlink{vonUnge02}{von Unge 02}) is a generalization of [[T-duality]] from [[fiber bundles]] equipped with an [[abelian group]] of [[isometries]] ([[torus]] [[bundles]]) to those with a [[nonabelian group]] of isometries.

Poisson-Lie T-duality may also be made manifest at the level of [[type II supergravity ]] in the framework of [[double field theory]] on [[Lie group|group manifolds]]. Using this framework both the NS/NS sector and the R/R sector are captured, and this allows to derive the transformation of the [[RR fields]] for full Poisson-Lie T-duality (\hyperlink{Hassler17}{Hassler 17}).

\hypertarget{as_a_partial_duality_of_string_theory}{}\subsection*{{As a partial duality of string theory}}\label{as_a_partial_duality_of_string_theory}

While ordinary abelian [[T-duality]] is supposedly a full [[duality in string theory]], in particular in that it is an equivalence on the [[string perturbation series]] to all orders of the squared [[string length]]/[[Regge slope]] $\alpha'$ and the [[string coupling constant]] $g_s$, it has apparntly been shown by [[Martin Roček]] (citation?) that there are topological [[obstructions]] at higher [[genus of a surface|genus]] for non-abelian T-duality, letting it break down in higher orders of $g_s$; and already a genus-0 ([[tree level]]) it apparently breaks down for the [[open string]] (i.e. on punctured [[disks]]) at some order of $\alpha'$.

\hypertarget{related_lab_entries}{}\subsection*{{Related $n$Lab entries}}\label{related_lab_entries}

\begin{itemize}%
\item [[topological T-duality]]


\item [[spherical T-duality]]



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

The original articles are

\begin{itemize}%
\item Xenia C. de la Ossa, Fernando Quevedo, \emph{Duality Symmetries from Non--Abelian Isometries in String Theories}, Nucl.Phys. B403 (1993) 377-394 (\href{http://xxx.lanl.gov/abs/hep-th/9210021}{hep-th/9210021})


\item [[Ctirad Klimcik]], [[Pavol Ševera]], \emph{Dual non-Abelian duality and the Drinfeld double}, Physics Letters B, Volume 351, Issue 4, 1 June 1995, Pages 455-462 ()


\item [[Rikard von Unge]], \emph{Poisson-Lie T-plurality}, Journal of High Energy Physics, Volume 2002, JHEP07 (2002) (\href{https://arxiv.org/abs/hep-th/0205245}{arXiv:hep-th/0205245})



\end{itemize}
Review includes

\begin{itemize}%
\item I. Petr, \emph{From Buscher Duality to Poisson‐Lie T‐Plurality on Supermanifolds}, AIP Conference Proceedings 1307, 119 (2010) ()


\item [[Konstadinos Sfetsos]], \emph{Recent developments in non-Abelian T-duality in string theory}, Fortschr. Phys., Special Issue: Proceedings of the ``Schools and Workshops on Elementary Particle Physics and Gravity'' (CORFU 2010), 29 August -- 12 September 2010, Corfu (Greece) Volume59, Issue11‐12 (\href{https://arxiv.org/abs/1105.0537}{arXiv:1105.0537})



\end{itemize}
See also

\begin{itemize}%
\item Benjo Fraser, Dimitrios Manolopoulos, [[Konstantinos Sfetsos]], \emph{Non-Abelian T-duality and Modular Invariance} (\href{https://arxiv.org/abs/1805.03657}{arXiv:1805.03657})

\end{itemize}
Discussion of the duality at the level of [[type II supergravity]] [[equations of motion]] is (using [[Riemannian geometry]] of [[Courant algebroids]]) due to

\begin{itemize}%
\item [[Branislav Jurco]], [[Jan Vysoky]], \emph{Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle}, Journal of Geometry and Physics Volume 130, August 2018, Pages 1-26 (\href{https://arxiv.org/abs/1708.04079}{arXiv:1708.04079})

\end{itemize}
Discussion within a broader picture of [[duality in physics|dual]] [[higher gauge theories]], including 4d [[electric-magnetic duality]]:

\begin{itemize}%
\item [[Ján Pulmann]], [[Pavol Ševera]], [[Fridrich Valach]], \emph{A non-abelian duality for (higher) gauge theories} (\href{https://arxiv.org/abs/1909.06151}{arXiv:1909.06151})

\end{itemize}
See also

\begin{itemize}%
\item [[Pavol Ševera]], [[Fridrich Valach]], \emph{Courant algebroids, Poisson-Lie T-duality, and type II supergravities} (\href{https://arxiv.org/abs/1810.07763}{arXiv:1810.07763})


\item [[Falk Hassler]], \emph{Poisson-Lie T-Duality in Double Field Theory} (\href{https://arxiv.org/abs/1707.08624}{arXiv:1707.08624})



\end{itemize}
Discussion of nonabelian [[T-folds]]:

\begin{itemize}%
\item Mark Bugden, \emph{Non-abelian T-folds} (\href{https://arxiv.org/abs/1901.03782}{arXiv:1901.03782})

\end{itemize}
Discussion in [[cosmology]]:

\begin{itemize}%
\item Ladislav Hlavatý, Ivo Petr, \emph{Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations} (\href{https://arxiv.org/abs/1910.08436}{arxiv:1910.08436})

\end{itemize}
[[!redirects nonabelian T-duality]]

[[!redirects non-abelian T-duality]]



\end{document}