Non-semisimple and Complex Gaugings of N=16 Supergravity

TL;DR

This paper explores the construction and consistency of non-semisimple and complex gauge groups in three-dimensional maximal supergravity, expanding the known landscape of admissible gauge groups and their scalar potentials.

Contribution

It introduces a method to generate non-semisimple gauge groups from semisimple ones via singular boosts in E_{8(8)} and demonstrates the consistent gauging of complex groups like SO(8,C).

Findings

Generated non-semisimple gauge groups from known semisimple groups.

Identified consistent embeddings of complex gauge groups into E_{8(8)}.

Analyzed scalar potentials related to these gauge groups.

Abstract

Maximal and non-maximal supergravities in three dimensions allow for a large variety of semisimple (Chern-Simons) gauge groups. In this paper, we analyze non-semisimple and complex gauge groups that satisfy the pertinent consistency relations for a maximal (N=16) gauged supergravity to exist. We give a general procedure how to generate non-semisimple gauge groups from known admissible semisimple gauge groups by a singular boost within E_{8(8)}. Examples include the theories with gauge group SO(8) x T_{28} that describe the reduction of IIA/IIB supergravity on the seven-sphere. In addition, we exhibit two `strange embeddings' of the complex gauge group SO(8,C) into (real) E_{8(8)} and prove that both can be consistently gauged. We discuss the structure of the associated scalar potentials as well as their relation to those of D>3 gauged supergravities.