Black hole entropy and the renormalization group

TL;DR

This paper explores how the renormalization group approach can clarify the nature of black hole entropy, particularly the division between gravitational and quantum contributions, for free and interacting fields.

Contribution

It introduces an RG flow scale to partition black hole entropy into gravitational and quantum parts, advancing understanding of entropy's microscopic origins.

Findings

RG flow scale helps separate gravitational and quantum entropy contributions

Analysis for free fields demonstrates the partitioning approach

Interacting fields introduce complexities in the entropy decomposition

Abstract

Four decades after its first postulation by Bekenstein, black hole entropy remains mysterious. It has long been suggested that the entanglement entropy of quantum fields on the black hole gravitational background should represent at least an important contribution to the total Bekenstein-Hawking entropy, and that the divergences in the entanglement entropy should be absorbed in the renormalization of the gravitational couplings. In this talk, we describe how an improved understanding of black hole entropy is obtained by combining these notions with the renormalization group. By introducing an RG flow scale, we investigate whether the total entropy of the black hole can be partitioned in a "gravitational" part related to the flowing gravitational action, and a "quantum" part related to the unintegrated degrees of freedom. We describe the realization of this idea for free fields, and the complications and qualifications arising for interacting fields.