A Comment on the Geometric Entropy and Conical Space

TL;DR

This paper investigates the issues with defining geometric entropy in conical spaces, revealing that non-minimal coupling in scalar fields causes anomalies, and clarifies their origin through canonical analysis.

Contribution

It provides a detailed explanation of the anomalous behavior of geometric entropy in conical spaces for non-minimally coupled scalar fields, using canonical formulation.

Findings

Geometric entropy can be non-positive in conical spaces.

Non-minimal coupling causes anomalies in entropy calculations.

Canonical analysis clarifies the origin of these anomalies.

Abstract

It has been recently pointed out that a definition of the geometric entropy using the partition function in a conical space does not in general lead to a positive definite quantity. For a scalar field model with a non-minimal coupling we clarify the origin of the anomalous behavior from the viewpoint of the canonical formulation.