On the Magical Supergravities in Six Dimensions

TL;DR

This paper explores the structure and gaugings of magical supergravities in six dimensions, revealing unique gauge groups and new couplings linked to the symmetries of the Magic Square geometries.

Contribution

It provides a classification of gaugings in six-dimensional magical supergravities, identifying the gauge group structure and new couplings without hypermultiplet interactions.

Findings

Gauge group is uniquely determined by maximal commuting translations in SO(n_T,1).

New minimal and Yukawa couplings are derived.

Scalar potential is explicitly determined.

Abstract

Magical supergravities are a very special class of supergravity theories whose symmetries and matter content in various dimensions correspond to symmetries and underlying algebraic structures of the remarkable geometries of the Magic Square of Freudenthal, Rozenfeld and Tits. These symmetry groups include the exceptional groups and some of their special subgroups. In this paper, we study the general gaugings of these theories in six dimensions which lead to new couplings between vector and tensor fields. We show that in the absence of hypermultiplet couplings the gauge group is uniquely determined by a maximal set of commuting translations within the isometry group SO(n_T,1) of the tensor multiplet sector. Moreover, we find that in general the gauge algebra allows for central charges that may have nontrivial action on the hypermultiplet scalars. We determine the new minimal couplings, Yukawa couplings and the scalar potential.