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

TL;DR

This paper classifies all supersymmetric solutions in 3D U(1)^3 gauged supergravity, revealing new warped AdS_3 and dS_3 geometries, and explores their holographic duals and interpolating flows.

Contribution

It provides the complete set of supersymmetric solutions, including new timelike and null warped AdS_3 geometries, and analyzes their holographic RG flows and c-function candidates.

Findings

Identified new timelike warped AdS_3 (G"odel) and dS_3 solutions.

Constructed numerical interpolating solutions between fixed points.

Classified null-warped AdS_3 vacua with Schrodinger symmetry.

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 AdS_3 (G\"odel) and timelike warped dS_3 critical 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 AdS_3 vacua with Schrodinger z=2 symmetry exist. We construct non-supersymmetric spacelike warped AdS_3 geometries based on D3-branes.