Entanglement entropy, planar surfaces, and spectral functions

TL;DR

This paper derives a non-perturbative formula for the entanglement entropy across a plane in flat space using spectral functions, explores its variation under relevant operator deformations, and examines effects of background geometry deformations.

Contribution

It introduces a spectral function approach to entanglement entropy and analyzes its behavior under deformations and background geometry changes.

Findings

Universal entanglement entropy expressed via spectral functions.

Perturbative expansion for entropy change under relevant operators.

New universal terms from geometry and coupling mixing.

Abstract

We consider the universal part of entanglement entropy across a plane in flat space for a QFT, giving a non-perturbative expression in terms of a spectral function. We study the change in entanglement entropy under a deformation by a relevant operator, providing a pertrubative expansion where the terms are correlation functions in the undeformed theory. The entanglement entropy for free massive fermions and scalars easily follows. Finally, we study entanglement entropy across a plane in a background geometry that is a deformation of flat space, finding new universal terms arising from mixing of geometry and couplings of the QFT.