Renormalized Entanglement Entropy on Cylinder

TL;DR

This paper introduces a framework for calculating entanglement entropy in non-conformal field theories using the dilaton effective action, and demonstrates its application to a massive scalar field on a cylindrical geometry, revealing a monotonic decrease of the renormalized entanglement entropy along the RG flow.

Contribution

It develops a method to compute and regularize entanglement entropy for non-conformal theories on a cylinder, introducing the renormalized entanglement entropy (REE) and analyzing its behavior.

Findings

REE decreases monotonically with increasing mass.

Numerical calculations confirm the monotonic behavior of REE.

The framework applies to theories on cylindrical geometries.

Abstract

We develop a framework of calculating entanglement entropy for non-conformal field theories with the use of the dilaton effective action. To illustrate it, we locate a theory on a cylinder $\mathbb{R} \times \mathbb{S}^{2}$ and compute entanglement entropy of a cap-like region perturbatively with respect to the mass for a free massive scalar field. A renormalized entanglement entropy (REE) is proposed to regularize the ultraviolet divergence on the cylinder. We find that the REE decreases monotonically both in the small and large mass regions as the mass increases. We confirm all of these behaviors by the numerical calculations, which further shows the monotonic decrease of the REE in the entire renormalization group flow.