Renormalized Entanglement Entropy on Cylinder

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.

28 pages, 6 figures, v2: a new section on an interesting discrepancy added, some explanations clarified

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Cited by in corpus (3)

• Entanglement Entropy for $TT$ deformed CFT in general dimensions
• Inter-universal entanglement in a cyclic multiverse
• The Edge of Entanglement: Getting the Boundary Right for Non-Minimally Coupled Scalar Fields