Supersymmetric AdS4 black holes from matter-coupled N=3,4 gauged supergravities

TL;DR

This paper constructs new supersymmetric $AdS_4$ black hole solutions in matter-coupled $N=3$ and $N=4$ gauged supergravities, revealing holographic RG flows from 3D SCFTs to superconformal quantum mechanics.

Contribution

It provides explicit analytic solutions for supersymmetric $AdS_4$ black holes with various horizon geometries in matter-coupled $N=3$ and $N=4$ gauged supergravities, expanding the landscape of holographic duals.

Findings

Found $AdS_2\times H^2$ and $AdS_2\times S^2$ geometries with interpolating solutions.

Identified multiple $AdS_4$ vacua with different symmetry groups.

Constructed black hole solutions with spherical and hyperbolic horizons.

Abstract

We study supersymmetric $AdS_4$ black holes in matter-coupled $N=3$ and $N=4$ gauged supergravities in four dimensions. In $N=3$ theory, we consider $N=3$ gauged supergravity coupled to three vector multiplets and $SO(3)\times SO(3)$ gauge group. The resulting gauged supergravity admits two $N=3$ supersymmetric $AdS_4$ vacua with $SO(3)\times SO(3)$ and $SO(3)$ symmetries. We find an $AdS_2\times H^2$ solution with $SO(2)\times SO(2)$ symmetry and an analytic solution interpolating between this geometry and the $SO(3)\times SO(3)$ symmetric $AdS_4$ vacuum. For $N=4$ gauged supergravity coupled to six vector multiplets with $SO(4)\times SO(4)$ gauge group, there exist four supersymmetric $AdS_4$ vacua with $SO(4)\times SO(4)$, $SO(4)\times SO(3)$, $SO(3)\times SO(4)$ and $SO(3)\times SO(3)$ symmetries. We find a number of $AdS_2\times S^2$ and $AdS_2\times H^2$ geometries together with the solutions interpolating between these geometries and all, but the $SO(3)\times SO(3)$, $AdS_4$ vacua. These solutions provide a new class of $AdS_4$ black holes with spherical and hyperbolic horizons dual to holographic RG flows across dimensions from $N=3,4$ SCFTs in three dimensions to superconformal quantum mechanics within the framework of four-dimensional gauged supergravity.