The Central Charge of the Warped AdS^3 Black Hole

TL;DR

This paper explores the holographic duality of warped AdS^3 black holes, deriving constraints on the dual CFT's central charge and primary field dimensions using topological and quasinormal mode analyses.

Contribution

It generalizes Witten's topological arguments to warped AdS^3, constraining the warping factor and linking quasinormal modes to primary field dimensions.

Findings

Topological constraints restrict the warping factor to rational numbers.

In certain limits, the system approaches Witten's conjectured CFT with central charges multiple of 24.

The central charges depend on the warping factor and match asymptotic symmetry results.

Abstract

The AdS/CFT conjecture offers the possibility of a quantum description for a black hole in terms of a CFT. This has led to the study of general AdS^3 type black holes with a view to constructing an explicit toy quantum black hole model. Such a CFT description would be characterized by its central charge and the dimensions of its primary fields. Recently the expression for the central charges (C_L, C_R) of the CFT dual to the warped AdS^3 have been determined using asymptotic symmetry arguments. The central charges depend, as expected, on the warping factor. We show that topological arguments, used by Witten to constrain central charges for the BTZ black hole, can be generalized to deal with the warped AdS^3 case. Topology constrains the warped factor to be rational numbers while quasinormal modes are conjectured to give the dimensions of primary fields. We find that in the limit when warping is large or when it takes special rational values the system tends to Witten's conjectured unique CFT's with central charges that are multiples of 24.