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

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.