Generalised proofs of the first law of entanglement entropy

Abstract

In this paper we develop generalised proofs of the holographic first law of entanglement entropy using holographic renormalisation. These proofs establish the holographic first law for non-normalizable variations of the bulk metric, hence relaxing the boundary conditions imposed on variations in earlier works. Boundary and counterterm contributions to conserved charges computed via covariant phase space analysis have been explored previously. Here we discuss in detail how counterterm contributions are treated in the covariant phase approach to proving the first law. Our methodology would be applicable to generalizing other holographic information analyses to wider classes of gravitational backgrounds.

arXiv comment57 pages

References in corpus (27)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Towards a derivation of holographic entanglement entropy
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
• Thermodynamics of Asymptotically Locally AdS Spacetimes
• Holographic Entanglement Entropy for General Higher Derivative Gravity
• On the Description of the Riemannian Geometry in the Presence of Conical Defects
• Generalized entropy and higher derivative Gravity
• Covariant phase space with boundaries
• Distributional Geometry of Squashed Cones
• Entanglement entropy across a deformed sphere
• Tomography from Entanglement
• From conformal to Einstein Gravity
• On Shape Dependence and RG Flow of Entanglement Entropy
• Some results on the shape dependence of entanglement and Rényi entropies
• Entanglement Entropy for Relevant and Geometric Perturbations
• Renormalized entanglement entropy
• Aspects of The First Law of Complexity
• Einstein Gravity from Conformal Gravity in 6D
• Einstein-AdS action, renormalized volume/area and holographic Renyi entropies
• A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow
• Shape dependence of renormalized holographic entanglement entropy
• Renormalized entanglement entropy and curvature invariants
• Non-conformal entanglement entropy