Supersymmetric deformations of 3D SCFTs from tri-Sasakian truncation

We holographically study supersymmetric deformations of \(N=3\) and \(N=1\) superconformal field theories in three dimensions using four-dimensional \(N=4\) gauged supergravity coupled to three-vector multiplets with non-semisimple \(SO(3)\ltimes (\mathbf {T}^3,\hat{\mathbf {T}}^3)\) gauge group. This gauged supergravity can be obtained from a truncation of 11-dimensional supergravity on a tri-Sasakian manifold and admits both \(N=1,3\) supersymmetric and stable non-supersymmetric \(AdS_4\) critical points. We analyze the BPS equations for SO(3) singlet scalars in detail and study possible supersymmetric solutions. A number of RG flows to non-conformal field theories and half-supersymmetric domain walls are found, and many of them can be given analytically. Apart from these “flat” domain walls, we also consider \(AdS_3\)-sliced domain wall solutions describing two-dimensional conformal defects with \(N=(1,0)\) supersymmetry within the dual \(N=1\) field theory while this type of solutions does not exist in the \(N=3\) case.