Self-Dual Warped AdS$_3$ Black Holes

TL;DR

This paper explores a new class of non-extremal black hole solutions in three-dimensional topological massive gravity, demonstrating their thermodynamics, asymptotic symmetries, and dual conformal field theory correspondence, enriching warped AdS/CFT understanding.

Contribution

It introduces self-dual warped AdS$_3$ black holes with consistent boundary conditions, revealing their dual CFTs with non-zero left central charge and matching correlators.

Findings

Black hole entropy matches Cardy formula.

Asymptotic symmetry forms a single Virasoro algebra.

Scalar correlators agree with dual CFT predictions.

Abstract

We study a new class of solutions of three-dimensional topological massive gravity. These solutions can be taken as non-extremal black holes, with their extremal counterparts being discrete quotients of spacelike warped AdS$_3$ along the $U(1)_L$ isometry. We study the thermodynamics of these black holes and show that the first law is satisfied. We also show that for consistent boundary conditions, the asymptotic symmetry generators form only one copy of the Virasoro algebra with central charge $c_L = \frac{4\nu\ell}{G(\nu^2+3)}$, with which the Cardy formula reproduces the black hole entropy. We compute the real-time correlators of scalar perturbations and find a perfect match with the dual CFT predictions. Our study provides a novel example of warped AdS/CFT correspondence: the self-dual warped AdS$_3$ black hole is dual to a CFT with nonvanishing left central charge. Moreover our investigation suggests that the quantum topological massive gravity asymptotic to the same spacelike warped AdS$_3$ in different consistent ways may be dual to different 2D CFTs.