AdS₃ vacua and RG flows in three dimensional gauged supergravities

Abstract

We study AdS ₃ supersymmetric vacua in N = 4 and N = 8, three dimensional gauged supergravities, with scalar manifolds ${\left( {\frac{{{\text{SO}}\left( {4,4} \right)}}{{{\text{SO}}(4) \times {\text{SO}}(4)}}} \right)^2}$ and $\frac{{{\text{SO}}\left( {8,8} \right)}}{{{\text{SO}}(8) \times {\text{SO}}(8)}}$, non-semisimple Chern-Simons gaugings SO(4) ⋉ R ⁶ and (SO(4) ⋉ R ⁶)², respectively. These are in turn equivalent to SO(4) and SO(4) × SO(4) Yang-Mills theories coupled to supergravity. For the N = 4 case, we study renormalization group flows between UV and IR AdS ₃ vacua with the same amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an analytic solution whereas in another, with (2,0) supersymmetry, we give a numerical solution. In both cases, the flows turn out to be v.e.v. flows, i.e. they are driven by the expectation value of a relevant operator in the dual SCFT ₂. These provide examples of v.e.v. flows between two AdS ₃ vacua within a gauged supergravity framework.