Entanglement Entropy Flow and the Ward Identity

Abstract

We derive differential equations for the flow of entanglement entropy as a function of the metric and the couplings of the theory. The variation of the universal part of entanglement entropy under a local Weyl transformation is related to the variation under a local change in the couplings. We show that this relation is in fact equivalent to the trace Ward identity. As a concrete application of our formalism, we express the entanglement entropy for massive free fields as a two-point function of the energy-momentum tensor.

arXiv comment4 pages; minor clarifications and references added

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• Entanglement Entropy for Relevant and Geometric Perturbations
• Area terms in entanglement entropy
• Renormalization group flow of entanglement entropy on spheres
• Holographic entanglement entropy in the nonconformal medium
• Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation
• Thermodynamic law from the entanglement entropy bound
• On the Shape Dependence of Entanglement Entropy
• Entanglement entropy and differential entropy for massive flavors
• Entanglement and RG in the $O(N)$ vector model
• Holographic RG flows, entanglement entropy and the sum rule
• What's the Point? Hole-ography in Poincare AdS
• The Edge of Entanglement: Getting the Boundary Right for Non-Minimally Coupled Scalar Fields
• Holographic Entanglement Entropy of Anisotropic Minimal Surfaces in LLM Geometries
• Holographic Approach to Entanglement Entropy in Disordered Systems
• Universal Terms of Entanglement Entropy for 6d CFTs
• Conformal a-charge, correlation functions and conical defects
• Composite operators in $T\bar{T}$-deformed free QFTs
• Sine-Gordon Theory : Entanglement entropy and holography
• More on Holographic Volumes, Entanglement, and Complexity
• Relative Entropy and Torsion Coupling
• OPE of the stress tensors and surface operators
• Universal terms of the entanglement entropy in a static closed universe
• Entanglement, Trace Anomaly and Confinement in QCD