Black hole entanglement entropy and the renormalization group

Abstract

We investigate the contributions of quantum fields to black hole entropy by using a cutoff scale at which the theory is described with a Wilsonian effective action. For both free and interacting fields, the total black hole entropy can be partitioned into a contribution derived from the gravitational effective action and a contribution from quantum fluctuations below the cutoff scale. In general the latter includes a quantum contribution to the Noether charge. We analyze whether it is appropriate to identify the rest with horizon entanglement entropy, and find several complications for this interpretation, which are especially problematic for interacting fields.

30 pages; v2, matches published version at PRD. Two references added, minor changes including additional remarks on the distinction between Euclidean and Lorentzian momentum cutoffs, on the degree of nonlocality in the effective action, and on the possibility that only the total entropy has an entanglement interpretation