Black hole entropy and SU(2) Chern-Simons theory

TL;DR

This paper demonstrates a manifestly SU(2) invariant approach to black hole entropy using Chern-Simons theory, clarifying state counting and deriving entropy proportional to horizon area with logarithmic corrections.

Contribution

It introduces a first-principles SU(2) invariant method for counting black hole states via Chern-Simons theory, resolving previous controversies.

Findings

Black hole entropy is proportional to horizon area a_H.

Logarithmic corrections to entropy are identified as -3/2 log a_H.

State counting is related to SU(2) intertwiners and Chern-Simons Hilbert spaces.

Abstract

Black holes in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with marked points. Moreover, the counting can be mapped to counting the number of SU(2) intertwiners compatible with the spins that label the defects. The resulting BH entropy is proportional to a_H with logarithmic corrections \Delta S=-3/2 \log a_H. Our treatment from first principles completely settles previous controversies concerning the counting of states.