Renormalized entanglement entropy

Abstract

We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement entropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renormalization group flows. The renormalized entanglement entropy for disk regions in $Ad{S}_4$ spacetimes agrees precisely with the holographically renormalized action for $Ad{S}_4$ with spherical slicing and hence with the F quantity, in accordance with the Casini-Huerta-Myers map. We present a generic class of holographic RG flows associated with deformations by operators of dimension $3/2<\Delta <5/2$ for which the F quantity increases along the RG flow, hence violating the strong version of the F theorem. We conclude by explaining how the renormalized entanglement entropy can be derived directly from the renormalized partition function using the replica trick i.e. our renormalization method for the entanglement entropy is inherited directly from that of the partition function. We show explicitly how the entanglement entropy counterterms can be derived from the standard holographic renormalization counterterms for asymptotically locally anti-de Sitter spacetimes.

arXiv comment44 pages

References in corpus (40)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• 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
• AdS/CFT Correspondence and Symmetry Breaking
• Generalized gravitational entropy
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• Wilson Loops and Minimal Surfaces
• Entanglement as a Probe of Confinement
• Hidden Fermi surfaces in compressible states of gauge-gravity duality
• Real-time gauge/gravity duality: Prescription, Renormalization and Examples
• Entanglement entropy, conformal invariance and extrinsic geometry
• A refinement of entanglement entropy and the number of degrees of freedom
• Conformal Anomaly Of Submanifold Observables In AdS/CFT Correspondence
• F-Theorem without Supersymmetry
• Universal terms for the entanglement entropy in 2+1 dimensions
• Entanglement Entropy from a Holographic Viewpoint
• Precision holography for non-conformal branes
• Hidden supersymmetry of domain walls and cosmologies
• Holographic Renormalization of general dilaton-axion gravity
• Entanglement and alpha entropies for a massive scalar field in two dimensions
• Anomalies, Conformal Manifolds, and Spheres
• Holographic renormalization as a canonical transformation
• Entanglement entropy in higher derivative holography
• Probing renormalization group flows using entanglement entropy
• On Shape Dependence and RG Flow of Entanglement Entropy
• General properties of holographic entanglement entropy
• Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors
• Weyl anomaly for Wilson surfaces
• Higher Derivative Corrections to R-charged Black Holes: Boundary Counterterms and the Mass-Charge Relation
• Non-Supersymmetric Membrane Flows from Fake Supergravity and Multi-Trace Deformations
• Hamilton-Jacobi Counterterms for Einstein-Gauss-Bonnet Gravity
• Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?
• Entanglement Entropy for Probe Branes
• Relevant Perturbation of Entanglement Entropy and Stationarity
• Generalized gravitational entropy of probe branes: flavor entanglement holographically
• Holographic renormalization and anisotropic black branes in higher curvature gravity
• Entanglement entropy and differential entropy for massive flavors

Cited by in corpus (45)

• Entanglement entropy: holography and renormalization group
• Entanglement Wedge Reconstruction and Entanglement of Purification
• Surface Counterterms and Regularized Holographic Complexity
• Towards Bulk Metric Reconstruction from Extremal Area Variations
• Comments on Holographic Entanglement Entropy in TT Deformed CFTs
• Probing phase transitions of holographic entanglement entropy with fixed area states
• Holographic Entanglement Negativity for Adjacent Subsystems in $\mathrm{Ad}{\mathrm{S}}_{\mathrm{d}+1}/CF{\mathrm{T}}_{\mathrm{d}}$
• c-theorem of the entanglement entropy
• Holographic Entanglement Entropy in the QCD Phase Diagram with a Critical Point
• Linear response of entanglement entropy from holography
• Free Energy of a Heavy Quark-Antiquark Pair in a Thermal Medium from AdS/CFT
• Entanglement entropy and $T\bar{T}$ deformations beyond antipodal points from holography
• Holographic RG flows on curved manifolds and the $F$-theorem
• Renormalized Volume
• Non-local observables at finite temperature in AdS/CFT
• Einstein-AdS action, renormalized volume/area and holographic Renyi entropies
• RG flow of entanglement entropy to thermal entropy
• Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
• A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow
• Topological terms, AdS_2n gravity and renormalized Entanglement Entropy of holographic CFTs
• The Quantum Null Energy Condition in Curved Space
• State-Dependent Divergences in the Entanglement Entropy
• Renormalization of Entanglement Entropy from topological terms
• Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
• Holographic torus entanglement and its RG flow
• Renormalized holographic entanglement entropy for Quadratic Curvature Gravity
• On Holographic Entanglement Density
• Does horizon entropy satisfy a Quantum Null Energy Conjecture?
• On actions for (entangling) surfaces and DCFTs
• Renormalized entanglement entropy and curvature invariants
• Entanglement entropy in scalar field theory and ${\mathbb{Z}}_M$ gauge theory on Feynman diagrams
• Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators
• What's the Point? Hole-ography in Poincare AdS
• Energy functionals from Conformal Gravity
• CFT correlators from shape deformations in Cubic Curvature Gravity
• Holographic Approach to Entanglement Entropy in Disordered Systems
• Non-conformal entanglement entropy
• Entanglement entropy of singular surfaces under relevant deformations in holography
• On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures
• Renormalized Holographic Subregion Complexity under Relevant Perturbations
• Conical defects and holography in topological AdS gravity
• Generalised proofs of the first law of entanglement entropy
• Entanglement entropy and complexity of singular subregions in deformed CFT
• Euclidean and complex geometries from real-time computations of gravitational Rényi entropies
• Holographic Entanglement Entropy for Brane-World Higher Derivative Gravity