Abstract
This is an extended version of the previous paper arXiv:2103.05303 to study entanglement entropy (EE) of a half space in interacting field theories. In the previous paper, we have proposed a novel method to calculate EE based on the notion of $\mathbb{Z}_M$ gauge theory on Feynman diagrams, and shown that EE consists of two particular contributions, one from a renormalized two-point correlation function in the two-particle irreducible (2PI) formalism and another from interaction vertices. In this paper, we further investigate them in more general field theories and show that the non-Gaussian contributions from vertices can be interpreted as renormalized correlation functions of composite operators.
Highlights
Over the past few decades, entanglement entropy (EE) has attracted much interest in various fields
We have proposed a novel method to calculate EE based on the notion of ZM gauge theory on Feynman diagrams, and shown that EE consists of two particular contributions, one from a renormalized two-point correlation function in the two-particle irreducible (2PI) formalism and another from interaction vertices
In our previous paper [58] we showed that the Gaussian part of EE is given by a renormalized two-point correlation function in the two-particle irreducible (2PI) formalism [59,60] and UV divergences specific to interactions are appropriately taken into account
Summary
Over the past few decades, entanglement entropy (EE) has attracted much interest in various fields. Interactions generally bring about two important consequences in QFTs: renormalization of IR quantities and non-Gaussianity of the vacuum wave function. In our previous paper [58] we showed that the Gaussian part of EE is given by a renormalized two-point correlation function in the two-particle irreducible (2PI) formalism [59,60] and UV divergences specific to interactions are appropriately taken into account. It is not the end of the story of EE in interacting theories.
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