Twisted Kac-Moody Algebras And The Entropy Of AdS$_3$ Black Hole

TL;DR

This paper demonstrates that a twisted Kac-Moody algebra derived from a Chern-Simons formulation accurately accounts for the entropy of AdS3 black holes, aligning with previous symmetry-based results.

Contribution

It introduces a twisted Kac-Moody algebra framework within Chern-Simons theory to describe AdS3 black hole entropy, extending the understanding of boundary symmetries.

Findings

Boundary WZNW theory yields two twisted Kac-Moody algebras.

Central charge matches that of the untwisted theory.

Asymptotic density of states aligns with Strominger's results.

Abstract

We show that an $SL(2,R)_L \times SL(2,R)_R$ Chern-Simons theory coupled to a source on a manifold with the topology of a disk correctly describes the entropy of the AdS$_3$ black hole. The resulting boundary WZNW theory leads to two copies of a twisted Kac-Moody algebra, for which the respective Virasoro algebras have the same central charge $c$ as the corresponding untwisted theory. But the eigenvalues of the respective $L_0$ operators are shifted. We show that the asymptotic density of states for this theory is, up to logarithmic corrections, the same as that obtained by Strominger using the asymptotic symmetry of Brown and Henneaux.