Deriving covariant holographic entanglement

Abstract

We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Renyi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.

arXiv comment39 pages. 9 figures

References in corpus (36)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Aspects of Holographic Entanglement Entropy
• A Covariant Holographic Entanglement Entropy Proposal
• Eternal Black Holes in AdS
• Towards a derivation of holographic entanglement entropy
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Generalized gravitational entropy
• Quantum corrections to holographic entanglement entropy
• Bulk Locality and Quantum Error Correction in AdS/CFT
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Relative entropy equals bulk relative entropy
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• The Gravity Dual of a Density Matrix
• Causality & holographic entanglement entropy
• Spacelike Branes
• The Gravity Dual of Renyi Entropy
• Holographic Entanglement Entropy for General Higher Derivative Gravity
• Real-time gauge/gravity duality: Prescription, Renormalization and Examples
• Real-time gauge/gravity duality
• Generalized entropy and higher derivative Gravity
• Holographic Calculations of Renyi Entropy
• Proof of the Holographic Formula for Entanglement Entropy
• Remarks on the entanglement entropy for disconnected regions
• Causal Holographic Information
• A Second Law for Higher Curvature Gravity
• The Fluid Manifesto: Emergent symmetries, hydrodynamics, and black holes
• General properties of holographic entanglement entropy
• Entanglement entropy in three dimensional gravity
• Generalized gravitational entropy without replica symmetry
• The imaginary part of the gravity action and black hole entropy
• Covariant Residual Entropy
• A paucity of bulk entangling surfaces: AdS wormholes with de Sitter interiors
• Topological aspects of generalized gravitational entropy
• Complex Entangling Surfaces for AdS and Lifshitz Black Holes?

Cited by in corpus (180)

• Replica Wormholes and the Entropy of Hawking Radiation
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
• The entropy of Hawking radiation
• Circuit complexity in quantum field theory
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Comments on Holographic Complexity
• Entanglement entropy: holography and renormalization group
• On the Time Dependence of Holographic Complexity
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Constraints on symmetry from holography
• On entanglement spreading in chaotic systems
• Circuit complexity for free fermions
• Islands in Schwarzschild black holes
• Codimension two holography for wedges
• Islands in Asymptotically Flat 2D Gravity
• Flat entanglement spectra in fixed-area states of quantum gravity
• Entanglement Entropy in Flat Holography
• Holographic Pseudo Entropy
• Entropy, Extremality, Euclidean Variations, and the Equations of Motion
• Schwinger-Keldysh formalism I: BRST symmetries and superspace
• Decoding the Apparent Horizon: A Coarse-Grained Holographic Entropy
• Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
• Observations of Hawking radiation: the Page curve and baby universes
• Complexity of Mixed States in QFT and Holography
• Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
• Replica wormholes for an evaporating 2D black hole
• Global symmetry, Euclidean gravity, and the black hole information problem
• Entanglement Wedge Reconstruction and Entanglement of Purification
• Geometric Aspects of Holographic Bit Threads
• Path integral optimization as circuit complexity
• Coarse Graining Holographic Black Holes
• Islands and stretched horizon
• Complexity Equals Anything II
• Modifications to Holographic Entanglement Entropy in Warped CFT
• The central dogma and cosmological horizons
• Open quantum systems and Schwinger-Keldysh holograms
• Holographic subregion complexity under a thermal quench
• Aspects of capacity of entanglement
• Probing Hawking radiation through capacity of entanglement
• Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories
• Fine structure in holographic entanglement and entanglement contour
• Replica wormholes and capacity of entanglement
• Towards Bulk Metric Reconstruction from Extremal Area Variations
• Page curves for a family of exactly solvable evaporating black holes
• Holographic Entanglement and Poincare blocks in three dimensional flat space
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Real-time gravitational replicas: Formalism and a variational principle
• Island for Gravitationally Prepared State and Pseudo Entanglement Wedge
• Entanglement negativity at large central charge
• Swing surfaces and holographic entanglement beyond AdS/CFT
• Holographic spacetime, black holes and quantum error correcting codes: A review
• Probing phase transitions of holographic entanglement entropy with fixed area states
• Microcanonical Path Integrals and the Holography of small Black Hole Interiors
• Quantum and Classical Correlations Inside the Entanglement Wedge
• Classification of out-of-time-order correlators
• Entanglement Wedge in Flat Holography and Entanglement Negativity
• Towards the generalized gravitational entropy for spacetimes with non-Lorentz invariant duals
• Warped Information and Entanglement Islands in AdS/WCFT
• $T\bar{T}$, the entanglement wedge cross section, and the breakdown of the split property
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
• Island and Page curve for one-sided asymptotically flat black hole
• The Holographic Shape of Entanglement and Einstein's Equations
• Covariant holographic entanglement negativity for disjoint intervals in $Ad{S}_3/CF{T}_2$
• Entanglement negativity, reflected entropy, and anomalous gravitation
• Holographic coherent states from random tensor networks
• Bit threads, Einstein's equations and bulk locality
• Exact Gravity Duals for Simple Quantum Circuits
• Subsystem trace distance in low-lying states of $(1+1)$-dimensional conformal field theories
• Holographic scattering requires a connected entanglement wedge
• The Page curve and baby universes
• The PEE aspects of entanglement islands from bit threads
• Holographic entanglement negativity for disjoint intervals in $Ad{S}_3/CF{T}_2$
• Evolution of Entanglement Wedge Cross Section Following a Global Quench
• Geometric Interpretation of Timelike Entanglement Entropy
• Calibrated Entanglement Entropy
• Complexity and entanglement in non-local computation and holography
• On de Sitter future-past extremal surfaces and the "entanglement wedge"
• Mixed State Entanglement for Holographic Axion Model
• Barrier from chaos: operator entanglement dynamics of the reduced density matrix
• Entanglement of Purification in Holographic Systems
• Microcanonical Action and the Entropy of Hawking Radiation
• Long-distance entanglement of purification and reflected entropy in conformal field theory
• Holographic second laws of black hole thermodynamics
• On the Role of Counterterms in Holographic Complexity
• Quantum Null Geometry and Gravity
• The holographic entropy cone from marginal independence
• A Holographic Argument for the Penrose Inequality in AdS
• Gravitation in flat spacetime from entanglement
• Constraining braneworlds with entanglement entropy
• The Quantum Null Energy Condition in Curved Space
• CFT sewing as the dual of AdS cut-and-paste
• Area Law Unification and the Holographic Event Horizon
• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• Radial Cutoffs and Holographic Entanglement
• The connected wedge theorem and its consequences
• Holographic Entanglement Entropy on Generic Time Slices
• The Boundary Dual of Bulk Local Operators
• Mixed State Entanglement and Thermal Phase Transitions
• Black Hole and de Sitter Microstructures from a Semiclassical Perspective
• Informational properties for Einstein-Maxwell-Dilaton Gravity
• Entropy of causal diamond ensembles
• Disentangling the gravity dual of Yang-Mills theory
• Time Evolution of Entanglement Negativity from Black Hole Interiors
• Bootstrapping Quantum Extremal Surfaces I: The Area Operator
• Entanglement island, miracle operators and the firewall
• Informational properties of holographic Lifshitz field theory
• All the entropies on the light-cone
• Restricted Maximin surfaces and HRT in generic black hole spacetimes
• More of the Bulk from Extremal Area Variations
• Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
• Entanglement negativity in $\text{T}\bar{\text{T}}$-deformed CFT${}_2$s
• A First Law of Entanglement Rates from Holography
• Entanglement Wedge Minimum Cross-section in Holographic Massive Gravity Theory
• Algebras and Hilbert spaces from gravitational path integrals: Understanding Ryu-Takayanagi/HRT as entropy without AdS/CFT
• Entanglement wedge cross-section in shock wave geometries
• Rényi Mutual Information in Holographic Warped CFTs
• Outer Entropy and Quasilocal Energy
• Discrete Gravity on Random Tensor Network and Holographic Rényi Entropy
• The Spacetime Geometry of Fixed-Area States in Gravitational Systems
• Saturation of the Quantum Null Energy Condition in Far-From-Equilibrium Systems
• Entanglement entropy and vacuum states in Schwarzschild geometry
• Gravity from entanglement for boundary subregions
• Quantum bit threads and holographic entanglement
• Large-$d$ phase transitions in holographic mutual information
• Interplay of entanglement structures and stabilizer entropy in spin models
• Metric Perturbations of Extremal Surfaces
• What's the Point? Hole-ography in Poincare AdS
• The holographic dual of Rényi relative entropy
• Holographic entanglement entropy is cutoff-covariant
• Holographic Entanglement Entropy of the Coulomb Branch
• On minimal entanglement wedge cross section for holographic entanglement negativity
• Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics
• Mixed-state Entanglement for AdS Born-Infeld Theory
• Entanglement Wedge Cross Section with Gauss-Bonnet Corrections and Thermal Quench
• The Holographic Entropy Cone in AdS-Vaidya Spacetimes
• Odd entanglement entropy in $\text{T}\bar{\text{T}}$ deformed CFT${}_2$s and holography
• Time-independent wormholes
• Minimal Areas from Entangled Matrices
• Holevo Information of Black Hole Mesostates
• $dS$ extremal surfaces, replicas, boundary Renyi entropies in $dS/CFT$ and time entanglement
• Topological string entanglement
• Non-analyticity of holographic Rényi entropy in Lovelock gravity
• Banados and SUSY: On Supersymmetry and Minimal Surfaces of Locally AdS3 Geometries
• The entanglement entropy of typical pure states and replica wormholes
• Mixed state entanglement in deformed field theory at finite temperature
• Subsystem entropy in 2d CFT and KdV ETH
• Rényi entropy at large energy density in 2D CFT
• Constraining higher order gravities with subregion duality
• Holographic entanglement entropy of the double Wick rotated BTZ black hole
• Charge transport properties in a novel holographic quantum phase transition model
• Measuring Holographic Entanglement Entropy on a Quantum Simulator
• Reconstruction of an AdS Radiation/Boson Star Bulk Geometry Using Light-cone Cuts
• Sine-Gordon Theory : Entanglement entropy and holography
• Holographic Entanglement Entropy for Gravitational Anomaly in Four Dimensions
• Entanglement Entropy with a Time-dependent Hamiltonian
• Upper bounds of holographic entanglement entropy growth rate for thermofield double states
• The Markov gap for geometric reflected entropy
• First Law and Quantum Correction for Holographic Entanglement Contour
• Entanglement in conformal field theory and holography
• Revisit the entanglement entropy with gravitational anomaly
• Weaving the (AdS) spaces with partial entanglement entropy threads
• Relational bulk reconstruction from modular flow
• Entanglement island and Page curve for one-sided charged black hole
• Entanglement Negativity in Flat Holography
• Non-trivial saddles in microscopic description of black holes
• Diagnosing quantum phase transition via holographic entanglement entropy at finite temperature
• Complexity of Magnetization and Magnetic Simplification
• Mutual information and holographic entanglement entropy for strongly-coupled R-charged plasmas
• Covariant odd entanglement entropy in AdS${}_3$/CFT${}_2$
• Holographic entanglement negativity for disjoint subsystems in $\mathrm{Ad}{\mathrm{S}}_{\mathrm{d}+1}/CF{\mathrm{T}}_{\mathrm{d}}$
• Holographic entanglement negativity for a single subsystem in conformal field theories with a conserved charge
• Euclidean and complex geometries from real-time computations of gravitational Rényi entropies
• Position dependence of the holographic entanglement entropy for an accelerating quark-antiquark pair
• Bulk entanglement and its shape dependence
• Entropy of Hawking Radiation for Two-Sided Hyperscaling Violating Black Branes
• Holography for de Sitter bubble geometries
• Holography in Quark-Gluon Plasma and Neutron Stars
• The generalized first law for more general matter
• Entanglement Renyi entropy of two disjoint intervals for large $c$ Liouville field theory