Renormalization of Entanglement Entropy and the Gravitational Effective Action
Abstract: The entanglement entropy associated with a spatial boundary in quantum field theory is UV divergent, its leading term being proportional to the area of the boundary. Callan and Wilczek proposed a geometrical prescription for computing this entanglement entropy as the response of the gravitational effective action to a conically singular metric perturbation. I demonstrate that the Callan-Wilczek prescription is rigorously justified for a particular class of quantum states, each expressible as a Euclidean path integral. I then show that the entanglement entropy is rendered UV finite by precisely the counterterms required to cancel the UV divergences in the gravitational effective action. In particular, the leading contribution to the entanglement entropy is given by the renormalized Bekenstein-Hawking formula. These results apply to a general quantum field theory coupled to a fixed background metric, holding for arbitrary entangling surfaces in any dimension, to all orders in perturbation theory in the quantum fields, and for all subleading UV divergent terms in the entanglement entropy. I also reconcile these results on the entanglement entropy with the existing literature, compare them to the Wald entropy, and speculate on their interpretation and implication.
1:30pm-2:30pm calendar page