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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.
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.
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
Leonardo Castellani, Lie derivatives along antisymmetric tensors, and the M-theory superalgebra (arXiv)
Urs Schreiber, SuGra 3-connection reloaded (blog)
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)