Non-semisimple gauging of a magical N=4 supergravity in three dimensions

TL;DR

This paper constructs a new three-dimensional N=4 supergravity model with a non-semisimple gauge group, revealing its vacuum structure, scalar mass spectrum, and potential higher-dimensional origin.

Contribution

It introduces a novel non-semisimple gauged supergravity in three dimensions with explicit scalar manifold and gauge group, including analysis of vacua and marginal deformations.

Findings

Existence of maximally supersymmetric AdS3 vacuum with SO(4) symmetry

Identification of half-supersymmetric domain wall solutions

Scalar potential has flat directions indicating marginal deformations

Abstract

We construct a new $N=4$ non-semisimple gauged supergravity in three dimensions with $E_{6(2)}/SU(6)\times SU(2)$ scalar manifold and $SO(4)\ltimes \mathbf{T}^6$ gauge group. Depending on the values of the gauge coupling constants, the theory admits both the maximally supersymmetric $AdS_3$ vacuum preserving $SO(4)$ gauge symmetry and half-supersymmetric domain walls with unbroken $SO(4)$ symmetry. We give all scalar masses at the supersymmetric $AdS_3$ critical point corresponding to an $N=(4,0)$ superconformal field theory (SCFT) in two dimensions. The scalar potential also admits two flat directions corresponding to marginal deformations that preserve full supersymmetry and conformal symmetry. This $SO(4)\ltimes \mathbf{T}^6$ gauged supergravity is expected to arise from a dimensional reduction on a three-sphere of the minimal $N=(1,0)$ supergravity in six dimensions coupled to three tensor and four vector multiplets.