The maximal D=7 supergravities

TL;DR

This paper presents a comprehensive formulation of seven-dimensional maximal supergravity using an embedding tensor approach, unifying various gaugings and including examples from M-theory and string theory reductions.

Contribution

It introduces a universal Lagrangian framework for 7D maximal supergravity characterized by an embedding tensor, capturing all possible gaugings and their group-theoretic structure.

Findings

Unified description of all gaugings in 7D supergravity

Inclusion of vector, two-form, and three-form fields with gauge invariance

Examples from M-theory and string theory reductions

Abstract

The general seven-dimensional maximal supergravity is presented. Its universal Lagrangian is described in terms of an embedding tensor which can be characterized group-theoretically. The theory generically combines vector, two-form and three-form tensor fields that transform into each other under an intricate set of nonabelian gauge transformations. The embedding tensor encodes the proper distribution of the degrees of freedom among these fields. In addition to the kinetic terms the vector and tensor fields contribute to the Lagrangian with a unique gauge invariant Chern-Simons term. This new formulation encompasses all possible gaugings. Examples include the sphere reductions of M theory and of the type IIA/IIB theories with gauge groups SO(5), CSO(4,1), and SO(4), respectively.