Group manifold approach to supergravity

TL;DR

This paper reviews the group-geometric approach to supergravity, emphasizing the unification of symmetries into superdiffeomorphisms on supergroup manifolds, with detailed example of N=1 supergravity in four dimensions.

Contribution

It provides a concise overview of recent developments in supergravity via the group manifold approach, illustrating the construction of actions using superdiffeomorphisms.

Findings

Unified description of symmetries in supergravity

Explicit construction of supergravity actions on supergroup manifolds

Clarification of geometric and integration concepts on supermanifolds

Abstract

We present a short review of the group-geometric approach to supergravity theories, from the point of view of recent developments. The central idea is the unification of usual diffeomorphisms, gauge symmetries and supersymmetries into superdiffeomorphisms in a supergroup manifold. The example of $N=1$ supergravity in $d=4$ is discussed in detail, and used to illustrate all the steps in the construction of a group manifold action. In the Appendices we summarize basic notions of group manifold geometry, and of integration on supermanifolds.