Emergent gravity and entanglement entropy of black holes

When the gravitational interaction emerges from some underlying quantum field theory, black hole entropy should be completely explained in terms of the entanglement entropy (EE) of the quantum fields. We show that this is the case of the anti-de Sitter black hole in two spacetime dimensions. In this case two-dimensional (2D) Newton constant is wholly induced by a conformal field theory and an exact formula for the EE can be derived. In the large black hole mass limit the leading term of this formula reproduces exactly the Bekenstein-Hawking entropy of the hole, whereas the subleading term behaves logarithmically. This subleading term has the universal form of the entanglement entropy of physical systems described by effective conformal fields theories (e.g. one-dimensional statistical models at the critical point).