Holographic entropy of Warped-AdS$_3$ black holes

TL;DR

This paper investigates the asymptotic symmetries of Warped-AdS3 spaces in New Massive Gravity, revealing an infinite-dimensional algebra structure and matching black hole entropy with dual Warped Conformal Field Theory calculations.

Contribution

It identifies the asymptotic symmetry algebra of WAdS3 in NMG as a semidirect sum of Virasoro and affine u(1) algebras and demonstrates the microscopic derivation of black hole entropy via WCFT.

Findings

Asymptotic symmetry algebra is a Virasoro plus affine u(1) structure.

Black hole entropy matches the WCFT Cardy formula.

Black hole configurations organize into two commuting Virasoro algebras.

Abstract

We study the asymptotic symmetries of three-dimensional Warped Anti-de Sitter (WAdS) spaces in three-dimensional New Massive Gravity (NMG). For a specific choice of asymptotic boundary conditions, we find that the algebra of charges is infinite-dimensional and coincides with the semidirect sum of Virasoro algebra with non-vanishing central charge and an affine $\hat{u}(1)_k$ Ka\v{c}-Moody algebra. We show that the WAdS black hole configurations organize in terms of two commuting Virasoro algebras. We identify the Virasoro generators that expand the associated representations in the dual Warped Conformal Field Theory (WCFT) and, by applying the Warped version of the Cardy formula, we prove that the microscopic WCFT computation exactly reproduces the entropy of black holes in WAdS space.