BTZ entropy from topological M-theory

Abstract

By determining the relation between topological M-theory and the Chern-Simons actions for a gauge field constructed from the Lie algebra of either SL(2, R) × SL(2, R) or SL(2, C) × SL(2, C), depending on the sign of the space-time curvature, we show that the standard and exotic actions of 3-dimensional gravity can be recovered from topological M-theory. With this result, we provide a concrete realisation of a conjecture by Dijkgraaf et al. stating that the partition function of topological M-theory is equivalent to the partition function of a black hole in a related theory. We do this for the standard and exotic BTZ black holes in 3-dimensional gravity