BTZ entropy from topological M-theory

TL;DR

This paper links topological M-theory to 3D gravity actions, demonstrating that the BTZ black hole partition functions can be derived from topological M-theory, thus supporting a conjecture relating these theories.

Contribution

It establishes a concrete connection between topological M-theory and 3D gravity actions, including BTZ black holes, confirming a conjecture about their partition functions.

Findings

Derived standard and exotic 3D gravity actions from topological M-theory.

Showed the equivalence of partition functions for BTZ black holes and topological M-theory.

Supported the conjecture relating topological M-theory to black hole partition functions.

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)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 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.