# Supersymmetric $AdS_5$ black holes and strings from 5D $N=4$ gauged supergravity

## TL;DR

This paper explores new supersymmetric solutions in five-dimensional N=4 gauged supergravity, including black strings and holes with specific near horizon geometries, extending known solutions and providing holographic RG flows for dual SCFTs.

## Contribution

It identifies a new class of supersymmetric $AdS_3$ and $AdS_2$ solutions in 5D N=4 gauged supergravity with various gauge groups, broadening the landscape of known black brane solutions.

## Key findings

- Discovery of new supersymmetric $AdS_3$ and $AdS_2$ solutions.
- Numerical holographic RG flows for twisted compactifications.
- Extension of known black string and black hole solutions.

## Abstract

We study supersymmetric $AdS_3\times \Sigma_2$ and $AdS_2\times \Sigma_3$ solutions, with $\Sigma_2=S^2,H^2$ and $\Sigma_3=S^3,H^3$, in five-dimensional $N=4$ gauged supergravity coupled to five vector multiplets. The gauge groups considered here are $U(1)\times SU(2)\times SU(2)$, $U(1)\times SO(3,1)$ and $U(1)\times SL(3,\mathbb{R})$. For $U(1)\times SU(2)\times SU(2)$ gauge group admiting two supersymmetric $N=4$ $AdS_5$ vacua, we identify a new class of $AdS_3\times \Sigma_2$ and $AdS_2\times H^3$ solutions preserving four supercharges. Holographic RG flows describing twisted compactifications of $N=2$ four-dimensional SCFTs dual to the $AdS_5$ vacua to the SCFTs in two and one dimensions dual to these geometries are numerically given. The solutions can also be interpreted as supersymmetric black strings and black holes in asymptotically $AdS_5$ spaces with near horizon geometries given by $AdS_3\times \Sigma_2$ and $AdS_2\times H^3$, respectively. These solutions broaden previously known black brane solutions including half-supersymmetric $AdS_5$ black strings recently found in $N=4$ gauged supergravity. Similar solutions are also studied in non-compact gauge groups $U(1)\times SO(3,1)$ and $U(1)\times SL(3,\mathbb{R})$.