Quantum Black Hole Entropy

TL;DR

This paper derives an exact formula for the boundary Hilbert space dimension in SU(2) Chern-Simons theory, providing a key step towards understanding black hole entropy in quantum gravity.

Contribution

It presents a novel exact calculation linking Chern-Simons boundary states to black hole entropy, advancing the quantum gravity approach to black hole thermodynamics.

Findings

Exact formula for boundary Hilbert space dimension

Connection to Bekenstein-Hawking entropy for Schwarzschild black holes

Relation between Chern-Simons states and conformal blocks

Abstract

We derive an exact formula for the dimensionality of the Hilbert space of the boundary states of SU(2) Chern-Simons theory, which, according to the recent work of Ashtekar et al, leads to the Bekenstein-Hawking entropy of a four dimensional Schwarzschild black hole. Our result stems from the relation between the (boundary) Hilbert space of the Chern-Simons theory with the space of conformal blocks of the Wess-Zumino model on the boundary 2-sphere.