Bekenstein-Hawking entropy as topological entanglement entropy

Abstract

Black holes in 2+1 dimensions enjoy long range topological interactions similar to those of non-abelian anyon excitations in a topologically ordered medium. Using this observation, we compute the topological entanglement entropy of BTZ black holes via the established formula S-top = log(S-0(a)), with S-b(a) the modular S-matrix of the Virasoro characters chi(a)(tau). We find a precise match with the Bekenstein-Hawking entropy. This result adds a new twist to the relationship between quantum entanglement and the interior geometry of black holes. We generalize our result to higher spin black holes, and again find a detailed match. We comment on a possible alternative interpretation of our result in terms of boundary entropy.