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\begin{document}

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\section*{D=3 supergravity}

[[!redirects 3-dimensional supergravity]]

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

\hypertarget{gravity}{}\paragraph*{{Gravity}}\label{gravity}

[[!include gravity contents]]

\hypertarget{physics}{}\paragraph*{{Physics}}\label{physics}

[[!include physicscontents]]

\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{PossibleGaugings}{Possible gaugings}\dotfill \pageref*{PossibleGaugings} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak
\noindent\hyperlink{generally}{Generally}\dotfill \pageref*{generally} \linebreak
\noindent\hyperlink{branes}{Branes}\dotfill \pageref*{branes} \linebreak
\noindent\hyperlink{gauged}{Gauged}\dotfill \pageref*{gauged} \linebreak


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

([[gauged supergravity|gauged]]) [[supergravity]] in [[dimension]] 3.

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

\hypertarget{PossibleGaugings}{}\subsubsection*{{Possible gaugings}}\label{PossibleGaugings}

The ([[U-duality]]-)[[global gauge group]] of maximally [[supersymmetry|supersymmetric]] 3d supergravity is [[E8]] (its [[split real form]] $E_{8(8)}$). Various [[subgroups]] of this may be promoted to [[local gauge groups]] (with [[gauge fields]] in [[gauged supergravity]]), which may be obtained via ([[flux compactification|fluxed]]) [[KK-compactification]] of [[11-dimensional supergravity]]. However, 3d supergravity also admits a maximal gauging where all of $E_{8(8)}$ is promoted to a local gauge group (\hyperlink{NicolaiSamtleben00}{Nicolai-Samtleben 00}, \hyperlink{NicolaiSamtleben01}{Nicolai-Samtleben 01, table 1})). This maximal gauging in 3d supergravity is not obtained by reduction from standard [[11-dimensional supergravity]], see the remarks in (\hyperlink{NicolaiSamtleben01}{Nicolai-Samtleben 01, section 7}) and see the followup (\hyperlink{HohmSamtleben13}{Hohm-Samtleben 13}). In (\hyperlink{deWitNicolai13}{de Wit-Nicolai 13, section 13}) it is suggested that the seemingly missing degrees of freedom necessary to accomplish for [[U-duality]]-gauge enhancement after reduction may be sitting in a [[non-perturbative effect|non-perturvative]] [[electric-magnetic duality|dual]] of the [[graviton]] ([[dual graviton]]).

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

\begin{itemize}%
\item [[11-dimensional supergravity]]


\item 10-dimensional [[type II supergravity]], [[heterotic supergravity]]


\item [[7-dimensional supergravity]]


\item [[5-dimensional supergravity]]


\item [[4-dimensional supergravity]]


\item \textbf{3-dimensional supergravity}

\begin{itemize}%
\item [[M-theory on 8-manifolds]]


\item [[3d quantum gravity]]



\end{itemize}

\item [[ABJM model]]



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

\hypertarget{generally}{}\subsubsection*{{Generally}}\label{generally}

Lecture notes include

\begin{itemize}%
\item F. Ruiz Ruiz, [[Peter van Nieuwenhuizen]], \emph{Lectures on Supersymmetry and Supergravity in $2+1$ Dimensions and regularization of supersymmetric gauge theories} (\href{http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.17.3667&rep=rep1&type=pdf}{pdf})

\end{itemize}
A complete list of un-gauged supergravities in 3 dimensions was given in

\begin{itemize}%
\item [[Bernard de Wit]], A.K. Tollsten, [[Hermann Nicolai]], \emph{Locally supersymmetric D=3 non-linear sigma models}, Nucl. Phys. B392 (1993) 3 (\href{http://xxx.lanl.gov/abs/hep-th/9208074}{arXiv:hep-th/9208074})

\end{itemize}
See also

\begin{itemize}%
\item Gabriele Tartaglino-Mazzucchelli, \emph{Topics in $3D$ $N=2$ AdS supergravity in superspace}, (\href{http://arxiv.org/abs/1202.0109}{arXiv:1202.0109})


\item Martin Pol\'a{}ek, [[Warren Siegel]], \emph{T-duality off shell in 3D Type II superspace} (\href{http://arxiv.org/abs/1403.6904}{arXiv:1403.6904})



\end{itemize}
\hypertarget{branes}{}\subsubsection*{{Branes}}\label{branes}

Discussion of [[D-branes]] in 3d supergravity includes

\begin{itemize}%
\item Bj\"o{}rn Brinne, Svend E. Hjelmeland, [[Ulf Lindström]], \emph{World-Volume Locally Supersymmetric Born-Infeld Actions}, Phys.Lett. B459 (1999) 507-514 (\href{http://arxiv.org/abs/hep-th/9904175}{arXiv:hep-th/9904175})


\item Bj\"o{}rn Brinne, \emph{3D supergravity and a spinning D2-brane}



\end{itemize}
\hypertarget{gauged}{}\subsubsection*{{Gauged}}\label{gauged}

Topological gauged supergravity in dimension three was first considered in

\begin{itemize}%
\item A. Ach\'u{}carro and [[Paul Townsend]], \emph{A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories}, Phys. Lett. B180 (1986) 89

\end{itemize}
Gauged supergravity via [[KK-compactification]] of [[11-dimensional supergravity]] on an 8-torus and with global [[E8]] [[U-duality]] and local $SO(16)$ [[gauge field]] was discussed in

\begin{itemize}%
\item [[Bernard Julia]], \emph{Application of supergravity to gravitation theories}, in \emph{Unified field theories in more than 4 dimensions} (V. D. Sabbata and E. Schmutzer, eds.), (Singapore), pp. 215--236, World Scientific, 1983.


\item N. Marcus, [[John Schwarz]], \emph{Three-dimensional supergravity theories}, Nucl. Phys. B228 (1983) 145.



\end{itemize}
The maximally supersymmetric gauged 3d supergravitites (and their \hyperlink{PossibleGaugings}{exceptional gaugings}) are listed in

\begin{itemize}%
\item [[Hermann Nicolai]], [[Henning Samtleben]], \emph{Maximal gauged supergravity in three dimensions}, Phys.Rev.Lett. 86 (2001) 1686-1689 (\href{http://xxx.lanl.gov/abs/hep-th/0010076}{arXiv:hep-th/0010076})

\end{itemize}
with details in

\begin{itemize}%
\item [[Hermann Nicolai]], [[Henning Samtleben]], \emph{Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions} (\href{http://arxiv.org/abs/hep-th/0103032}{arXiv:hep-th/0103032})


\item [[Olaf Hohm]], [[Henning Samtleben]], \emph{Exceptional Form of $D=11$ Supergravity}, Phys. Rev. Lett. 111, 231601 (2013) (\href{http://arxiv.org/abs/1308.1673}{arXiv:1308.1673})


\item [[Bernard de Wit]], [[Hermann Nicolai]], \emph{Deformations of gauged SO(8) supergravity and supergravity in eleven dimensions} (\href{http://arxiv.org/abs/1302.6219}{arXiv:1302.6219})



\end{itemize}
(see also at \emph{[[exceptional generalized geometry]]}).

See also

\begin{itemize}%
\item Hitoshi Nishino, Subhash Rajpoot, \emph{Topologican Gauging of N=16 Supergravity in Three-Dimensions}, Phys.Rev. D67 (2003) 025009 (\href{http://arxiv.org/abs/hep-th/0209106}{arXiv:hep-th/0209106})


\item Eoin \'O{} Colg\'a{}in, [[Henning Samtleben]], \emph{3D gauged supergravity from wrapped M5-branes with AdS/CMT applications}, JHEP 1102:031,2011 (\href{http://arxiv.org/abs/1012.2145}{arXiv:1012.2145})


\item Edi Gava, Parinya Karndumri, K. S. Narain, \emph{3D gauged supergravity from SU(2) reduction of N=1 6D supergravity}, JHEP 09 (2010) 028 (\href{http://arxiv.org/abs/1006.4997}{arXiv:1006.4997})



\end{itemize}
[[!redirects 3-dimensional supergravities]]

[[!redirects 3d supergravity]] [[!redirects 3d supergravities]]



\end{document}