Gauged Supergravities in Various Spacetime Dimensions

TL;DR

This review explores the structure and classification of gauged supergravity theories across various dimensions, emphasizing the role of the embedding tensor in maintaining supersymmetry and gauge invariance, with applications to string compactifications.

Contribution

It provides a comprehensive overview of the embedding tensor formalism in gauged supergravities, detailing its group-theoretical constraints and applications to multiple supergravity models.

Findings

Classified all possible gaugings compatible with supersymmetry.

Connected higher-dimensional origins to lower-dimensional gaugings.

Illustrated how fluxes and torsion are embedded in the tensor.

Abstract

In this review articel we study the gaugings of extended supergravity theories in various space-time dimensions. These theories describe the low-energy limit of non-trivial string compactifications. For each theory under consideration we review all possible gaugings that are compatible with supersymmetry. They are parameterized by the so-called embedding tensor which is a group theoretical object that has to satisfy certain representation constraints. This embedding tensor determines all couplings in the gauged theory that are necessary to preserve gauge invariance and supersymmetry. The concept of the embedding tensor and the general structure of the gauged supergravities are explained in detail. The methods are then applied to the half-maximal (N=4) supergravities in d=4 and d=5 and to the maximal supergravities in d=2 and d=7. Examples of particular gaugings are given. Whenever possible, the higher-dimensional origin of these theories is identified and it is shown how the compactification parameters like fluxes and torsion are contained in the embedding tensor.