Entanglement entropy in scalar field theory and ZM gauge theory on Feynman diagrams

Entanglement entropy (EE) in interacting field theories has two important issues: renormalization of UV divergences and non-Gaussianity of the vacuum. In this paper, 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 Z(M) gauge theory on Feynman diagrams: 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.

Automated summary

In this paper, the entanglement entropy in interacting scalar field theory is investigated using the two-particle irreducible formalism. The concept of EE is formulated as a Z(M) gauge theory on Feynman diagrams, where Z(M) fluxes are assigned on plaquettes and summed to obtain EE. The Gaussian part of EE is expressed in terms of a renormalized 2-point function, while the non-Gaussianity of the vacuum is reflected in the vertices.