# nLab Supergravity and Superstrings - A Geometric Perspective

### Context

#### Gravity

gravity, supergravity

superalgebra

and

supergeometry

## Applications

This entry is about the textbook

on supergravity and string theory with an emphasis on the D'Auria-Fre formulation of supergravity.

At the time of this writing the book is out of print and unavailable from bookshops. But your local physics department library may have a copy.

## Description

This book focuses on the discussion of supergravity-aspects of string theory from the point of view of the D'Auria-Fre formulation of supergravity. 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 infinity-connections with values in super L-infinity algebras such as the supergravity Lie 3-algebra.

See also higher category theory and physics.

## Further references

The original article that introduced th D’Auria-Fré-formalism is

The geometric perspective discussed there is both the emphasis of working over base supermanifolds and combined with that the the approach that here we call tthe D’Auria-Fré-formalism .

The interpretation of the D’Auria-Fré-formalism in terms of ∞-Lie algebra valued forms together with a discussion of the supergravity Lie 3-algebra in the context of String Lie n-algebras was given in

This had been preceded by some blog discussion, for instance

This is, as far as I am aware, the first occurence of the explicit observation that the FDA-formalism is about higher gauge theory, based on hearing a talk on

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 I am aware, would be grateful for further references) is page 2 of

An attempt at a comprehensive discussion of the formalism in the context of cohesive (∞,1)-topos-theory for smooth super ∞-groupoids is in the last section of

Here are some more references:

• Pietro Fré, M-theory FDA, twisted tori and Chevalley cohomology (arXiv)

• Pietro Fré and Pietro Antonio Grassi, Pure spinors, free differential algebras, and the supermembrane (arXiv)

• Pietro Fré and Pietro Antonio Grassi, Free differential algebras, rheonomy, and pure spinors (arXiv)

category: reference

Revised on August 31, 2011 02:18:00 by Urs Schreiber (131.211.239.100)