Hidden Conformal Symmetry of Self-Dual Warped AdS_3 Black Holes in Topological Massive Gravity

TL;DR

This paper demonstrates the presence of hidden conformal symmetry in self-dual warped AdS3 black holes within topological massive gravity, linking wave equations to dual CFT predictions and matching entropy and scattering results.

Contribution

It extends the hidden conformal symmetry framework to self-dual warped AdS3 black holes, revealing symmetry breaking patterns and supporting the dual CFT correspondence.

Findings

Wave equation matches SL(2,R) Casimir operator

Left conformal symmetry is broken to U(1)

Entropy and scattering match dual CFT predictions

Abstract

We extend the recently proposal of hidden conformal symmetry to the self-dual warped AdS$_3$ black holes in topological massive gravity. It is shown that the wave equation of massive scalar field with sufficient small angular momentum can be reproduced by the SL(2, R) Casimir quadratic operator. Due to the periodic identification in the $\phi$ direction, it is found that only the left section of hidden conformal symmetry is broken to U(1), while the right section is unbroken, which only gives the left temperature of dual CFT. As a check of the dual CFT conjecture of self-warped AdS$_3$ black hole, we further compute the Bekenstein-Hawking entropy and absorption cross section and quasinormal modes of scalar field perturbation and show these are just of the forms predicted by the dual CFT.