Black Hole Entropy in the O(N) Model

TL;DR

This paper investigates quantum corrections to black hole entropy within an O(N) invariant scalar field model, revealing scale-dependent interpretations of entropy from entanglement to effective field descriptions.

Contribution

It introduces a novel calculation of black hole entropy corrections using a 1/N expansion in an O(N) scalar model, connecting entanglement and effective field perspectives.

Findings

Entropy from diagrams similar to string theory approaches.

At short distances, entropy has a state counting interpretation.

In the infrared, entropy interpretation shifts to an effective field perspective.

Abstract

We consider corrections to the entropy of a black hole from an $O(N)$ invariant linear $\s$-model. We obtain the entropy from a $1/N$ expansion of the partition function on a cone. The entropy arises from diagrams which are analogous to those introduced by Susskind and Uglum to explain black hole entropy in string theory. The interpretation of the \sm entropy depends on scale. At short distances, it has a state counting interpretation, as the entropy of entanglement of the $N$ fields $\pa$. In the infrared, the effective theory has a single composite field $\s \sim \pa \pa$, and the state counting interpretation of the entropy is lost.