On Lagrangians and Gaugings of Maximal Supergravities

TL;DR

This paper analyzes the group-theoretical structure of gaugings in maximal supergravity theories, focusing on the T-tensor's role and providing examples across different spacetime dimensions, including non-semisimple gaugings.

Contribution

It offers a comprehensive group-theoretical framework for understanding gaugings in maximal supergravity, including identities and examples in various dimensions.

Findings

Derived all relevant T-tensor identities in generality

Presented numerous examples of gaugings in 4 and 5 dimensions

Included non-semisimple gaugings from Scherk-Schwarz reductions

Abstract

A consistent gauging of maximal supergravity requires that the T-tensor transforms according to a specific representation of the duality group. The analysis of viable gaugings is thus amenable to group-theoretical analysis, which we explain and exploit for a large variety of gaugings. We discuss the subtleties in four spacetime dimensions, where the ungauged Lagrangians are not unique and encoded in an E_7(7)\Sp(56,R)/GL(28) matrix. Here we define the T-tensor and derive all relevant identities in full generality. We present a large number of examples in d=4,5 spacetime dimensions which include non-semisimple gaugings of the type arising in (multiple) Scherk-Schwarz reductions. We also present some general background material on the latter as well as some group-theoretical results which are necessary for using computer algebra.