Shape dependence of renormalized holographic entanglement entropy

Abstract

We study the holographic entanglement entropy of deformed entangling regions in three-dimensional CFTs dual to Einstein-AdS gravity, using a renormalization scheme based on the addition of extrinsic counterterms. In this prescription, when even-dimensional manifolds are considered, the universal contribution to the entanglement entropy is identified as the renormalized volume of the Ryu-Takayanagi hypersurface, which is written as the sum of a topological and a curvature term. It is shown that the change in the renormalized entanglement entropy due to the deformation of the entangling surface is encoded purely in the curvature contribution. In turn, as the topological part is given by the Euler characteristic of the Ryu-Takayanagi surface, it remains shape independent. Exploiting the covariant character of the extrinsic counterterms, we apply the renormalization scheme for the case of deformed entangling regions in AdS${}_4$/CFT${}_3$, recovering the results found in the literature. Finally, we provide a derivation of the relation between renormalized entanglement entropy and Willmore energy. The presence of a lower bound of the latter makes manifest the relation between the AdS curvature of the Ryu-Takayanagi surface and the strong subadditivity property.

arXiv comment31 pages, 3 figures, Final version for JHEP

References in corpus (73)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entanglement Entropy and Quantum Field Theory
• A Stress Tensor for Anti-de Sitter Gravity
• Aspects of Holographic Entanglement Entropy
• The Holographic Weyl anomaly
• A Covariant Holographic Entanglement Entropy Proposal
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Entanglement entropy and conformal field theory
• Towards a derivation of holographic entanglement entropy
• Cool horizons for entangled black holes
• Generalized gravitational entropy
• Surface Terms as Counterterms in the AdS/CFT Correspondence
• Entanglement entropy in free quantum field theory
• Holographic c-theorems in arbitrary dimensions
• Notes on Some Entanglement Properties of Quantum Field Theory
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• On the RG running of the entanglement entropy of a circle
• Seeing a c-theorem with holography
• Thermodynamics of Asymptotically Locally AdS Spacetimes
• The Gravity Dual of Renyi Entropy
• Holographic Entanglement Entropy
• The Gravitational Action in Asymptotically AdS and Flat Spacetimes
• Entanglement entropy, conformal invariance and extrinsic geometry
• Entanglement entropy: holography and renormalization group
• A refinement of entanglement entropy and the number of degrees of freedom
• On the Description of the Riemannian Geometry in the Presence of Conical Defects
• F-Theorem without Supersymmetry
• Holographic Local Quenches and Entanglement Density
• Universal terms for the entanglement entropy in 2+1 dimensions
• Causal Holographic Information
• Extremal surfaces as bulk probes in AdS/CFT
• AdS/CFT and Strong Subadditivity of Entanglement Entropy
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Distributional Geometry of Squashed Cones
• Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
• Mass, Angular Momentum and Thermodynamics in Four-Dimensional Kerr-AdS Black Holes
• Topological regularization and self-duality in four-dimensional anti-de Sitter gravity
• Conical geometry and quantum entropy of a charged Kerr black hole
• Dynamics of Entanglement Entropy from Einstein Equation
• Regularization of odd-dimensional AdS gravity: Kounterterms
• Rényi entropy and conformal defects
• Entanglement entropy across a deformed sphere
• Entanglement Entropy: A Perturbative Calculation
• Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions
• On Shape Dependence and RG Flow of Entanglement Entropy
• Entanglement Entropy for Singular Surfaces
• Universality in the geometric dependence of Renyi entropy
• Shape Dependence of Entanglement Entropy in Conformal Field Theories
• Some results on the shape dependence of entanglement and Rényi entropies
• Shape Dependence of Holographic Rényi Entropy in General Dimensions
• De Sitter Space and Entanglement
• Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories
• On entanglement entropy functionals in higher derivative gravity theories
• Entanglement density and gravitational thermodynamics
• Curvature, Cones, and Characteristic Numbers
• Universal entanglement for higher dimensional cones
• Renormalized AdS action and Critical Gravity
• Entanglement entropy for odd spheres
• What surface maximizes entanglement entropy?
• On shape dependence of holographic entanglement entropy in AdS4/CFT3
• Einstein-AdS action, renormalized volume/area and holographic Renyi entropies
• Generalizing the entanglement entropy of singular regions in conformal field theories
• A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow
• Topological terms, AdS_2n gravity and renormalized Entanglement Entropy of holographic CFTs
• Renormalization of Entanglement Entropy from topological terms
• An Inhomogeneous Jacobi equation for minimal surfaces and perturbative change of Holographic Entanglement Entropy
• Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
• On the Shape Dependence of Entanglement Entropy
• Entanglement susceptibilities and universal geometric entanglement entropy
• Conical Space-times: a Distributional Theory Approach
• Entanglement entropy from the holographic stress tensor
• Entanglement Entropy and Duality in AdS(4)
• Renormalized Holographic Subregion Complexity under Relevant Perturbations

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• Disks globally maximize the entanglement entropy in $2+1$ dimensions