Black hole entanglement entropy and the renormalization group

TL;DR

This paper explores how quantum fields contribute to black hole entropy using a Wilsonian effective action, highlighting the complexities in interpreting entanglement entropy, especially for interacting fields.

Contribution

It introduces a framework to separate black hole entropy into gravitational and quantum fluctuation parts using a cutoff scale, addressing the interpretation challenges.

Findings

Quantum contributions include a quantum Noether charge.

Interacting fields pose significant interpretation issues.

The total entropy can be partitioned into distinct contributions.

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.