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 Stop = log(S 0a), with Sba the modular S-matrix of the Virasoro characters Xa (τ). 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.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- Black holes
- Gauge-gravity correspondence
- Topological states of matter