AdS$_3$ vacua and RG flows in three dimensional gauged supergravities

TL;DR

This paper investigates supersymmetric $AdS_3$ vacua and RG flows in three-dimensional gauged supergravities with specific scalar manifolds and gaugings, providing analytic and numerical solutions for flows driven by operator expectation values.

Contribution

It presents the first detailed analysis of $AdS_3$ vacua and RG flows in N=4 and N=8 gauged supergravities with particular scalar manifolds and gaugings, including explicit solutions.

Findings

Analytic RG flow solution with (3,1) supersymmetry.

Numerical RG flow solution with (2,0) supersymmetry.

Flows are driven by expectation values of relevant operators.

Abstract

We study $AdS_3$ supersymmetric vacua in N=4 and N=8, three dimensional gauged supergravities, with scalar manifolds $(\frac{SO(4,4)}{SO(4)\times SO(4)})^2$ and $\frac{SO(8,8)}{SO(8)\times SO(8)}$, non-semisimple Chern-Simons gaugings $SO(4)\ltimes {\bf R}^6$ and $(SO(4)\ltimes {\bf R}^6)^2$, respectively. These are in turn equivalent to SO(4) and $SO(4)\times SO(4)$ 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.