A note on entanglement entropy and quantum geometry

It has been argued that the entropy computed in the isolated horizon framework of loop quantum gravity is closely related to the entanglement entropy of the gravitational field, and that the calculation performed is not restricted to horizons. We recall existing work on this issue and explain how recent work on generalizing these computations to arbitrary spacetime dimensions D + 1 >= 3 supports this point of view and makes the duality between entanglement entropy and the entropy computed from counting boundary states manifest. In a certain semiclassical regime in 3 + 1 dimensions, this entropy is given by the Bekenstein-Hawking formula.