The Edge of Entanglement: Getting the Boundary Right for Non-Minimally Coupled Scalar Fields

TL;DR

This paper investigates the correct boundary terms in entanglement calculations for non-minimally coupled scalar fields, clarifying previous ambiguities and extending understanding to related field theories.

Contribution

It provides a new derivation of boundary terms in entanglement entropy for non-minimally coupled scalars, resolving existing puzzles and exploring implications for other theories.

Findings

Boundary term derivation clarifies entanglement computations

Resolves mass correction and twist operator puzzles

Extends boundary term considerations to other field theories

Abstract

In entanglement computations for a free scalar field with coupling to background curvature, there is a boundary term in the modular Hamiltonian which must be correctly specified in order to get sensible results. We focus here on the entanglement in flat space across a planar interface and (in the case of conformal coupling) other geometries related to this one by Weyl rescaling of the metric. For these "half-space entanglement" computations, we give a new derivation of the boundary term and revisit how it clears up a number of puzzles in the literature, including mass corrections and twist operator dimensions. We also discuss how related boundary terms may show up in other field theories.