BTZ entropy from topological M-theory

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) x SL(2, R) or SL(2, C) x SL(2, C), depending on the sign of the space-time curvature, we show that the standard and exotic actions of three-dimensional gravity can be recovered from topological M-theory. With this result, we provide a concrete realization 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 three-dimensional gravity.