The Statistical Mechanics of the Three-Dimensional Euclidean Black Hole

Abstract

In its formulation as a Chern-Simons theory, three-dimensional general relativity induces a Wess-Zumino-Witten action on spatial boundaries. Treating the horizon of the three-dimensional Euclidean black hole as a boundary, I count the states of the resulting WZW model, and show that when analytically continued back to Lorentzian signature, they yield the correct Bekenstein-Hawking entropy. The relevant states can be understood as ``would-be gauge'' degrees of freedom that become dynamical at the horizon.

9 pages, LaTeX. Significant sign error corrected, continuation to Lorentzian signature clarified, several other clarifications (although conclusion is unaffected). To appear in Phys. Rev. D