Edge States and Entropy of 2d Black Holes

Abstract

In several recent publications Carlip, as well as Balachandran, Chandar and Momen, have proposed a statistical mechanical interpretation for black hole entropy in terms of ``would be gauge'' degrees of freedom that become dynamical on the boundary to spacetime. After critically discussing several routes for deriving a boundary action, we examine their hypothesis in the context of generic 2-D dilaton gravity. We first calculate the corresponding statistical mechanical entropy of black holes in 1+1 deSitter gravity, which has a gauge theory formulation as a BF-theory. Then we generalize the method to dilaton gravity theories that do not have a (standard) gauge theory formulation. This is facilitated greatly by the Poisson-Sigma-model formulation of these theories. It turns out that the phase space of the boundary particles coincides precisely with a symplectic leaf of the Poisson manifold that enters as target space of the Sigma-model. Despite this qualitatively appealing picture, the quantitative results are discouraging: In most of the cases the symplectic leaves are non-compact and the number of microstates yields a meaningless infinity. In those cases where the particle phase space is compact - such as, e.g., in the Euclidean deSitter theory - the edge state degeneracy is finite, but generically it is far too small to account for the semiclassical Bekenstein-Hawking entropy.