The Statistical Mechanics of the Three-Dimensional Euclidean Black Hole

TL;DR

This paper models the 3D Euclidean black hole as a boundary WZW theory derived from Chern-Simons formulation, successfully reproducing the Bekenstein-Hawking entropy by counting boundary states.

Contribution

It introduces a boundary WZW model approach to compute black hole entropy in 3D Euclidean gravity, connecting gauge degrees of freedom to horizon microstates.

Findings

Boundary states match Bekenstein-Hawking entropy

States are interpreted as gauge degrees of freedom becoming dynamical

Analytic continuation to Lorentzian signature yields correct entropy

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.