WAdS$_3$/CFT$_2$ correspondence in presence of bulk massive gravitons

TL;DR

This paper extends the WAdS$_3$/CFT$_2$ correspondence to include bulk massive gravitons, demonstrating that the dual CFT can account for additional degrees of freedom and reproduce black hole entropy.

Contribution

It introduces new boundary conditions allowing bulk gravitons in WAdS$_3$ spaces and shows the dual CFT captures these bulk degrees of freedom.

Findings

The asymptotic charge algebra includes Virasoro and Kac-Moody components.

The central charge matches the value needed to reproduce black hole entropy.

The correspondence holds even with the presence of bulk massive gravitons.

Abstract

In a previous paper, it has been shown that the entropy of non-extremal black holes in Warped Anti-de Sitter (WAdS) spaces in massive gravity can be computed microscopically in terms of a dual conformal field theory. Here, we extend this computation to a set of asymptotic boundary conditions that, while still gathering the WAdS$_3$ black holes, also allow for new solutions that are not locally equivalent to WAdS$_3$ space, and therefore are associated to the local degrees of freedom of the theory (bulk massive gravitons). After presenting explicit examples of such geometries, we compute the asymptotic charge algebra and show that it is generated by the semi-direct sum of Virasoro algebra and an affine Kac-Moody algebra. The value of the central charge turns out to be exactly the one that leads to reproduce the entropy of the WAdS$_3$ black holes. This result probes the WAdS$_3$/CFT$_2$ correspondence in presence of bulk gravitons.