Options for Gauge Groups in Five-Dimensional Supergravity

TL;DR

This work classifies the admissible gauge groups in five-dimensional $ ext{N}=2$ supergravity by analyzing the very special geometry encoded in the cubic coefficients $C_{ ilde{I} ilde{J} ilde{K}}$ and the interplay with tensor multiplets. The authors derive precise conditions on scalar fields in vector, tensor, and hypermultiplets for gauging a compact group $K$ (Abelian, semisimple, or semisimple$ imes$Abelian), showing that tensor multiplets forbid purely semisimple gauge groups and that hypermultiplet content affects allowable gaugings through quaternionic isometries. They provide constructive classifications of viable gaugings, including detailed treatments of $C_{ijk}$ deformations with and without tensor fields, and illustrate the formalism by embedding the Standard Model gauge group in a 5D $ ext{N}=2$ supergravity setting. The results offer a comprehensive toolkit for building 5D gauged supergravity models, with implications for extra-dimensional phenomenology and connections to AdS/Minkowski vacua depending on $U(1)_R$ gauging.

Abstract

Motivated by the possibility that physics may be effectively five-dimensional over some range of distance scales, we study the possible gaugings of five-dimensional N=2 supergravity. Using a constructive approach, we derive the conditions that must be satisfied by the scalar fields in the vector, tensor and hypermultiplets if a given global symmetry is to be gaugeable. We classify all those theories that admit the gauging of a compact group that is either Abelian or semi-simple, or a direct product of a semi-simple and an Abelian group. In the absence of tensor multiplets, either the gauge group must be semi-simple or the Abelian part has to be U(1)_R and/or an Abelian isometry of the hyperscalar manifold. On the other hand, in the presence of tensor multiplets the gauge group cannot be semi-simple. As an illustrative exercise, we show how the Standard Model SU(3) X SU(2) X U(1) group may be gauged in five-dimensional N=2 supergravity. We also show how previous special results may be recovered within our general formalism.