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\begin{document}

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\section*{Supergravity and Superstrings - A Geometric Perspective}

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

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

[[!include gravity contents]]

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

[[!include string theory - contents]]

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

[[!include physicscontents]]

\hypertarget{supergeometry}{}\paragraph*{{Supergeometry}}\label{supergeometry}

[[!include supergeometry - contents]]

This entry contains material related to the textbook

\begin{itemize}%
\item [[Leonardo Castellani]], [[Riccardo D'Auria]], [[Pietro Fré]],

\emph{Supergravity and Superstrings - A Geometric Perspective}

World Scientific, 1991



\end{itemize}
on [[supergravity]] and [[string theory]] with an emphasis on the [[D'Auria-Fré formulation of supergravity]], based on

\begin{itemize}%
\item [[Riccardo D'Auria]], [[Pietro Fré]] \emph{[[GeometricSupergravity.pdf:file]]}, Nuclear Physics B201 (1982) 101-140

\end{itemize}
The book is out of print, unfortunately, but check $gen.lib$. The newer book

\begin{itemize}%
\item [[Pietro Fré]], \emph{Gravity, a Geometrical Course: Volume 2: Black Holes, Cosmology and Introduction to Supergravity}, Springer 2012

\end{itemize}
is much more brief in comparison, but has more history and exposition, and treats more recent developments, such as aspects related to [[AdS-CFT]].

\hypertarget{description}{}\subsection*{{Description}}\label{description}

This book focuses on the discussion of [[supergravity]]-aspects of [[string theory]] from the point of view of the [[D'Auria-Fré formulation of supergravity]], which is implicitly a formulation via [[supergeometry|supergeometry]] [[higher Cartan geometry]]. Therefore, while far, far from being written in the style of a mathematical treatise, this book stands out as making a consistent proposal for what the central ingredients of a mathematical formalization might be: as explained at the above link, secretly this book is all about describing supergravity in terms of [[connection on an infinity-bundle|infinity-connections]] with values in [[super L-infinity algebra]]s such as the [[supergravity Lie 3-algebra]].

See also [[higher category theory and physics]].

\hypertarget{further_references}{}\subsection*{{Further references}}\label{further_references}

The original article that introduced the D'Auria-Fr\'e{}-formalism is

\begin{itemize}%
\item \textbf{geSuGra} R. D'Auria, P. Fr\'e{} \emph{Geometric supergravity in $D = 11$ and its hidden supergroup} [[GeometricSupergravity.pdf:file]]

\end{itemize}
The \emph{geometric perspective} discussed there is both the emphasis of working over base [[supermanifold]]s and combined with that the the approach that here we call the \emph{D'Auria-Fr\'e{}-formalism} .

The interpretation of the D'Auria-Fr\'e{}-formalism in terms of [[∞-Lie algebra valued forms]] together with a discussion of the [[supergravity Lie 3-algebra]] in the context of [[String Lie 2-algebra|String Lie n-algebra]]s was given in

\begin{itemize}%
\item [[Hisham Sati]], [[Urs Schreiber]], [[Jim Stasheff]], \emph{$L_\infty$-algebra connections} ()

\end{itemize}
Apart from that the first vague mention of the observation that the ``FDA''-formalism for supergravity is about higher categorical Lie algebras (as far as [[Urs Schreiber|I]] am aware, would be grateful for further references) is page 2 of

\begin{itemize}%
\item [[Pietro Fré]], [[Pietro Antonio Grassi]], \emph{Free differential algebras, rheonomy and pure spinors} (\href{http://arxiv.org/abs/0801.3076}{arXiv})

\end{itemize}
An attempt at a comprehensive discussion of the formalism in the context of [[cohesive (∞,1)-topos]]-theory for [[smooth super ∞-groupoid]]s is in the last section of

\begin{itemize}%
\item [[Urs Schreiber]], \emph{[[schreiber:differential cohomology in a cohesive topos]]}

\end{itemize}
Here are some more references:

\begin{itemize}%
\item [[Pietro Fré]], \emph{M-theory FDA, twisted tori and Chevalley cohomology} (\href{http://www.arxiv.org/abs/hep-th/0510068}{arXiv})


\item [[Pietro Fré]], Pietro Antonio Grassi, \emph{Pure spinors, free differential algebras, and the supermembrane} (\href{http://www.arxiv.org/abs/hep-th/0606171}{arXiv:hep-th/0606171})


\item [[Pietro Fré]] and Pietro Antonio Grassi, \emph{Free differential algebras, rheonomy, and pure spinors} (\href{http://www.arxiv.org/abs/0801.3076}{arXiv:0801.3076})



\end{itemize}
category: reference



\end{document}