Group manifold approach to supergravity

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.

27 pages. Invited chapter for the "Handbook of Quantum Gravity", Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer, expected in 2023. arXiv admin note: substantial text overlap with arXiv:1802.03407