Hidden Conformal Symmetry of Warped AdS_3 Black Holes

TL;DR

This paper reveals a hidden SL(2,R) symmetry in the wave equation of scalar fields around warped AdS_3 black holes, supporting the WAdS/CFT correspondence by matching temperatures and absorption cross sections.

Contribution

It uncovers a hidden conformal symmetry in warped AdS_3 black holes and relates it to dual CFT properties, providing new insights into the holographic structure.

Findings

Identified hidden SL(2,R) symmetry in scalar wave equations.

Derived dual CFT temperatures matching black hole parameters.

Confirmed absorption cross sections align with CFT two-point functions.

Abstract

We show that for a certain low frequency limit the wave equation of a generic massive scalar field in the background of the spacelike warped AdS_3 black hole can be written as the Casimir of an SL(2,R) symmetry. Two sets of SL(2,R) generators are found which uncover the hidden SL(2,R)\times SL(2,R) symmetry of the solution. This symmetry is only locally defined and is spontaneously broken to U(1)\times U(1) by a periodic identification of the \phi coordinate. By using the generator of the identification we read the left and right temperatures (T_L,T_R) of the proposed dual conformal field theory which are in complete agreement with the WAdS/CFT conjecture. Moreover, under the above condition of the scalar wave frequency, absorption cross section of the scalar field is consistent with the two-point function of the dual CFT.