The maximal D=4 supergravities

TL;DR

This paper systematically presents all maximal supergravity theories in four dimensions, detailing their Lagrangians, gauge structures, and duality properties, with a focus on the embedding tensor formalism and tensor gauge fields.

Contribution

It introduces a universal formulation of maximal supergravities using the embedding tensor and tensor gauge fields, unifying electric and magnetic duality descriptions.

Findings

Unified description of ungauged supergravities via E_7(7)/Sp(56,R)/GL(28) matrix

General class of supersymmetric, gauge-invariant Lagrangians derived

Framework accommodates magnetic charges and dual gauge fields

Abstract

All maximal supergravities in four space-time dimensions are presented. The ungauged Lagrangians can be encoded in an E_7(7)\Sp(56,R)/GL(28) matrix associated with the freedom of performing electric/magnetic duality transformations. The gauging is defined in terms of an embedding tensor which encodes the subgroup of E_7(7) that is realized as a local invariance. This embedding tensor may imply the presence of magnetic charges which require corresponding dual gauge fields. The latter can be incorporated by using a recently proposed formulation that involves tensor gauge fields in the adjoint representation of E_7(7). In this formulation the results take a universal form irrespective of the electric/magnetic duality basis. We present the general class of supersymmetric and gauge invariant Lagrangians and discuss a number of applications.