Abstract
This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of ZM gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. We have also shown that the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.
Highlights
Entanglement entropy (EE) captures correlations for bipartite entangled states between two subspaces, in particular spatially separated regions, and has been widely investigated in conformal field theories (CFTs) [1,2,3,4,5], perturbations from CFTs [6,7,8] or in the context of AdS/CFT correspondence [9,10,11,12]
We will investigate further issues of the renormalization group (RG) flow of EE in a separate paper [50]. This is the third paper in a series of our investigations on EE in interacting field theories based on the notion of the Z M gauge theory on Feynman diagrams, proposed in [42] and extended in [43]
We have focused on two important contributions to EE: one from the propagators of the fundamental field and another from vertices which can be interpreted as correlations of composite operators
Summary
Entanglement entropy (EE) captures correlations for bipartite entangled states between two subspaces, in particular spatially separated regions, and has been widely investigated in conformal field theories (CFTs) [1,2,3,4,5], perturbations from CFTs [6,7,8] or in the context of AdS/CFT correspondence [9,10,11,12] (for review, [12,13]). In [42], we succeeded to extract two particular contributions to EE in interacting field theories: one is the Gaussian contributions written in terms of renormalized two-point correlation functions in the two-particle irreducible (2PI) formalism. Another set of important contributions comes from classical vertices, which reflects non-Gaussianity of the vacuum wave function. The paper is organized as follows: in Section 2, we first briefly summarize the notion of the Z M gauge theory on Feynman diagrams, two particular contributions to EE from propagators and vertices in the φ4 scalar theory, and an interpretation of the vertex contribution in terms of a correlator of a composite operator. This is a generalization of the proof for the propagator contributions based on the 2PI formalism
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