Aspects of Warped AdS$_3$/CFT$_2$ Correspondence

TL;DR

This paper investigates the holographic duality between warped AdS$_3$ spacetimes and 2D conformal field theories in the context of topologically and new massive gravity, using thermodynamics and asymptotic symmetry analysis.

Contribution

It applies the thermodynamics method to warped black holes in massive gravity theories and proposes a new warped AdS$_3$/CFT$_2$ correspondence with explicit central charges.

Findings

Thermodynamics method yields consistent results with ASG analysis.

Develops a Mathematica implementation for asymptotic symmetry calculations.

Proposes a specific warped AdS$_3$/CFT$_2$ duality with explicit central charges.

Abstract

In this paper we apply the thermodynamics method to investigate the holographic pictures for the BTZ black hole, the spacelike and the null warped black holes in three-dimensional topologically massive gravity (TMG) and new massive gravity (NMG). Even though there are higher derivative terms in these theories, the thermodynamics method is still effective. It gives consistent results with the ones obtained by using asymptotical symmetry group (ASG) analysis. In doing the ASG analysis we develop a brute-force realization of the Barnich-Brandt-Compere formalism with Mathematica code, which also allows us to calculate the masses and the angular momenta of the black holes. In particular, we propose the warped AdS$_3$/CFT$_2$ correspondence in the new massive gravity, which states that quantum gravity in the warped spacetime could holographically dual to a two-dimensional CFT with $c_R=c_L=\f{24}{Gm\b^2\sr{2(21-4\b^2)}}$.