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

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.

arXiv comment7 pages, 8 figures; detailed derivations of equations and 4 figures added (v2); minor corrections, published version in PRD (v3)

References in corpus (48)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Aspects of Holographic Entanglement Entropy
• Scaling of Entanglement close to a Quantum Phase Transitions
• A Covariant Holographic Entanglement Entropy Proposal
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement in a simple quantum phase transition
• Holographic Entanglement Entropy: An Overview
• The Page curve of Hawking radiation from semiclassical geometry
• Entanglement entropy in free quantum field theory
• Entanglement entropy of black holes
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Introduction to Nonequilibrium Quantum Field Theory
• A refinement of entanglement entropy and the number of degrees of freedom
• Entanglement entropy in gauge theories and the holographic principle for electric strings
• Entanglement Entropy in the O(N) model
• AdS Bubbles, Entropy and Closed String Tachyons
• Holographic entanglement beyond classical gravity
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Entanglement entropy for the n-sphere
• Some Calculable Contributions to Entanglement Entropy
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Probing renormalization group flows using entanglement entropy
• Entanglement Entropy of a Massive Fermion on a Torus
• Twist operators in higher dimensions
• Entanglement Entropy for Relevant and Geometric Perturbations
• Observations on entanglement entropy in massive QFT's
• Entanglement Entropy in Scalar Field Theory
• Renormalized entanglement entropy
• Renyi Entanglement Entropy of Interacting Fermions Calculated Using Continuous-Time Quantum Monte Carlo Method
• Renormalization of Entanglement Entropy and the Gravitational Effective Action
• Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks
• Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
• Entanglement of Quantum Fluctuations in the Inflationary Universe
• Entanglement entropy, planar surfaces, and spectral functions
• Entanglement in Four-Dimensional SU(3) Gauge Theory
• Lattice study of Rényi entanglement entropy in $SU(N_c)$ lattice Yang-Mills theory with $N_c=2,3,4$
• Quantum chaos, thermalization and entanglement generation in real-time simulations of the BFSS matrix model
• Towards Spacetime Entanglement Entropy for Interacting Theories
• Entropy of a subalgebra of observables and the geometric entanglement entropy
• An Inverse Mass Expansion for Entanglement Entropy in Free Massive Scalar Field Theory
• Entanglement and RG in the $O(N)$ vector model
• Entanglement Entropy and Variational Methods: Interacting Scalar Fields
• Renormalized entanglement entropy and curvature invariants
• Entanglement Entropy: Non-Gaussian States and Strong Coupling

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