Anomalies, entropy and boundaries

TL;DR

This paper explores the relationship between conformal anomalies and entanglement entropy in odd-dimensional spacetimes with boundaries, revealing new logarithmic contributions when the entangling surface intersects the boundary.

Contribution

It demonstrates the existence of a logarithmic term in entanglement entropy in odd dimensions with boundaries and relates it to the integrated conformal anomaly, extending previous understanding.

Findings

Logarithmic term appears in entanglement entropy when the entangling surface crosses the boundary.

Distributional properties of boundary geometries are established in the presence of conical singularities.

Contributions to entropy depend on the angle between the boundary and the entangling surface.

Abstract

A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFT's in even dimensions. In odd dimensions the local anomaly and the logarithmic term in the entropy are absent. As was observed recently, there exists a non-trivial integrated anomaly if an odd-dimensional spacetime has boundaries. We show that, similarly, there exists a logarithmic term in the entanglement entropy when the entangling surface crosses the boundary of spacetime. The relation of the entanglement entropy to the integrated conformal anomaly is elaborated for three-dimensional theories. Distributional properties of intrinsic and extrinsic geometries of the boundary in the presence of conical singularities in the bulk are established. This allows one to find contributions to the entropy that depend on the relative angle between the boundary and the entangling surface.