Entanglement entropy in scalar field theory and $\mathbb{Z}_M$ gauge theory on Feynman diagrams

TL;DR

This paper explores entanglement entropy in interacting scalar field theories using a novel $ ext{Z}_M$ gauge theory approach on Feynman diagrams, addressing UV divergences and vacuum non-Gaussianity.

Contribution

It introduces a $ ext{Z}_M$ gauge theory framework on Feynman diagrams to analyze entanglement entropy, incorporating flux configurations as twists and separating Gaussian and non-Gaussian contributions.

Findings

EE expressed via renormalized 2-point functions

Flux configurations interpreted as propagator and vertex twists

Addresses UV divergence renormalization and vacuum non-Gaussianity

Abstract

Entanglement entropy (EE) in interacting field theories has two important issues: renormalization of UV divergences and non-Gaussianity of the vacuum. In this letter, we investigate them in the framework of the two-particle irreducible formalism. In particular, we consider EE of a half space in an interacting scalar field theory. It is formulated as $\mathbb{Z}_M$ gauge theory on Feynman diagrams: $\mathbb{Z}_M$ fluxes are assigned on plaquettes and summed to obtain EE. Some configurations of fluxes are interpreted as twists of propagators and vertices. The former gives a Gaussian part of EE written in terms of a renormalized 2-point function while the latter reflects non-Gaussianity of the vacuum.