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

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.