All supersymmetric solutions of 3D U(1)³ gauged supergravity

Abstract: D3-branes wrapping constant curvature Riemann surfaces give rise to 2D N=(0,2) SCFTs, where the superconformal fixed-points are mapped to vacua of 3D N=2 U(1)³ gauged supergravity. In this work we determine the fermionic supersymmetry variations of the theory and present all supersymmetric solutions. For spacetimes with a timelike Killing vector, we identify new timelike warped AdS₃ (Gödel) and timelike warped dS₃ fixed-points. We outline the construction of numerical solutions interpolating between fixed-points, demonstrate that these flows are driven by an irrelevant scalar operator in the SCFT and identify the inverse of the superpotential as a candidate c-function. We further classify all spacetimes with a null Killing vector, in the process producing loci in parameter space where null-warped AdS₃ vacua with Schrödinger z = 2 symmetry exist. We construct non-supersymmetric spacelike warped AdS₃ geometries based on D3-branes.