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# Entanglement Entropy in Interacting Field Theories

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### 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.

### Author and article information

###### Journal
09 March 2021
###### Article
2103.05303