General Matter Coupled N=4 Gauged Supergravity in Five Dimensions

TL;DR

The authors construct the most general matter-coupled ${\cal N}=4$ gauged supergravity in five dimensions, built from ungauged MESGTs with vector and tensor multiplets by gauging subgroups of $SO(5,n)\times SO(1,1)$. Abelian gaugings require dualizing charged vectors to self-dual tensor fields, with the Abelian factor limited to one dimension; semi-simple gaugings avoid tensors and embed into the adjoint of the gauge group. When both sectors are gauged, the scalar potential contains interference terms that can yield AdS vacua, in contrast to the pure Abelian or pure semi-simple cases which admit Minkowski vacua (under certain conditions). The results provide a comprehensive framework for exploring AdS/CFT-related RG flows and potential brane-world realizations within ${\cal N}=4$ supergravity, and lay groundwork for further vacua analyses and phenomenological explorations. These constructions unify prior isolated gaugings and offer explicit Lagrangians, SUSY transformations, and scalar potentials up to the relevant order. Key contributions include the classification of admissible gaugings, the introduction of tensor fields for Abelian gaugings, the explicit form of the combined scalar potential ${\cal V}$, and the demonstration that AdS vacua are possible only in the $K_S\times K_A$ setting with a one-dimensional Abelian factor, along with the identification of Minkowski vacua in special cases.

Abstract

We construct the general form of matter coupled N=4 gauged supergravity in five dimensions. Depending on the structure of the gauge group, these theories are found to involve vector and/or tensor multiplets. When self-dual tensor fields are present, they must be charged under a one-dimensional Abelian group and cannot transform non-trivially under any other part of the gauge group. A short analysis of the possible ground states of the different types of theories is given. It is found that AdS ground states are only possible when the gauge group is a direct product of a one-dimensional Abelian group and a semi-simple group. In the purely Abelian, as well as in the purely semi-simple gauging, at most Minkowski ground states are possible. The existence of such Minkowski ground states could be proven in the compact Abelian case.