Options for Gauge Groups in Five-Dimensional Supergravity

TL;DR

This paper classifies possible gauge groups in five-dimensional N=2 supergravity, exploring conditions for gauging symmetries and illustrating how the Standard Model gauge group can be embedded.

Contribution

It provides a comprehensive classification of gauge groups in five-dimensional N=2 supergravity, including conditions for gauging and examples like the Standard Model.

Findings

Classified gauge groups as Abelian, semi-simple, or products thereof.

Identified restrictions on gauge groups depending on tensor multiplet presence.

Demonstrated embedding of the Standard Model gauge group in this framework.

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.