Topological Entanglement Entropy of Black Hole Interiors

摘要

Recent theoretical progress shows that (2 t 1) black hole solution manifests long-range topo-logical quantum entanglement similar to exotic non-Abelian excitations with fractional quan-tum statistics. In topologically ordered systems, there is a deep connection between physics ofthe bulk and that at the boundaries. Boundary terms play an important role in explaining theblack hole entropy in general. We ˉnd several common properties between BTZ black holes andthe Quantum Hall e?ect in (2 t 1)-dimensional bulk/boundary theories. We calculate thetopological entanglement entropy of a (2 t 1) black hole and recover the Bekenstein–Hawkingentropy, showing that black hole entropy and topological entanglement entropy are related.Using Chern–Simons and Liouville theories, we ˉnd that long-range entanglement describes theinterior geometry of a black hole and identify it with the boundary entropy as the bond requiredby the connectivity of spacetime, gluing the short-range entanglement described by the arealaw. The IR bulk–UV boundary correspondence can be realized as a UV low-excitation theoryon the bulk matching the IR long-range excitations on the boundary theory. Several aspects ofthe current ˉndings are discussed.