The Gravity Dual of Renyi Entropy

Abstract

A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge/gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Renyi entropies. Here we show that all Renyi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Renyi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Renyi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.

9 pages, 1 figure; v2: typos fixed, references and minor clarifications added; v3: references added, title and format changed to match version to be published in Nature Communications

References in corpus (19)

• Towards a derivation of holographic entanglement entropy
• Area laws in quantum systems: mutual information and correlations
• Relative entropy equals bulk relative entropy
• Holographic duality from random tensor networks
• Entanglement entropy of two disjoint intervals in conformal field theory II
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Entanglement Entropy at Large Central Charge
• Universality of corner entanglement in conformal field theories
• Entropy and Entanglement in Quantum Ground States
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
• Universality in the geometric dependence of Renyi entropy
• Twist operators in higher dimensions
• Some results on the shape dependence of entanglement and Rényi entropies
• Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories
• Holographic Reconstruction of General Bulk Surfaces
• Renyi entropy, stationarity, and entanglement of the conformal scalar
• The holographic supersymmetric Renyi entropy in five dimensions
• Renyi Entropy and Geometry
• Topological aspects of generalized gravitational entropy

Cited by in corpus (227)

• Holographic duality from random tensor networks
• Out-of-Time-Order Correlation for Many-Body Localization
• Entanglement entropy: holography and renormalization group
• Deriving covariant holographic entanglement
• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Large N algebras and generalized entropy
• Entanglement entropy and $T\overline{T}$ deformation
• Flat entanglement spectra in fixed-area states of quantum gravity
• Entanglement Entropy in Flat Holography
• Entropy, Extremality, Euclidean Variations, and the Equations of Motion
• Holographic Pseudo Entropy
• Derivation of holographic negativity in AdS${}_3$/CFT${}_2$
• Holographic Renyi Entropy from Quantum Error Correction
• Schwinger-Keldysh formalism I: BRST symmetries and superspace
• De Sitter Holography and Entanglement Entropy
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Conformal field theories are magical
• Entanglement Entropy in $T\overline{T}$-Deformed CFT
• Area-law versus Rényi and Tsallis black hole entropies
• Complexity and the bulk volume, a new York time story
• Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
• Entanglement Wedge Cross Sections Require Tripartite Entanglement
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• Renyi Entropy of Chaotic Eigenstates
• Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK
• Entanglement Beyond $\mathrm{AdS}$
• Quantum Information in Holographic Duality
• Leading order corrections to the quantum extremal surface prescription
• Complexity Equals Anything II
• Effective entropy of quantum fields coupled with gravity
• Machine Learning Spatial Geometry from Entanglement Features
• Aspects of capacity of entanglement
• Probing Hawking radiation through capacity of entanglement
• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories
• Shape Dependence of Holographic Rényi Entropy in General Dimensions
• A New Proposal for Holographic BCFT
• Replica wormholes and capacity of entanglement
• Entanglement and Rényi Entropy of Multiple Intervals in $T\overline{T}$-Deformed CFT and Holography
• Holographic entanglement negativity and replica symmetry breaking
• Spacetime Fluctuations in AdS/CFT
• De Sitter Space and Entanglement
• On New Proposal for Holographic BCFT
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Real-time gravitational replicas: Formalism and a variational principle
• Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction
• Comments on Holographic Entanglement Entropy in TT Deformed CFTs
• An Exact Construction of Codimension two Holography
• On holographic time-like entanglement entropy
• Entanglement, quantum randomness, and complexity beyond scrambling
• Code properties from holographic geometries
• Conformal Description of Near-Horizon Vacuum States
• Quantum vs. classical information: operator negativity as a probe of scrambling
• The holographic entropy arrangement
• Symmetry-resolved entanglement in a long-range free-fermion chain
• A Holographic Proof of Rényi Entropic Inequalities
• Probing phase transitions of holographic entanglement entropy with fixed area states
• The Page Curve for Reflected Entropy
• Quantum algorithm for estimating Renyi entropies of quantum states
• Enhanced corrections near holographic entanglement transitions: a chaotic case study
• A new multi-partite entanglement measure and its holographic dual
• One-loop universality of holographic codes
• $T\bar{T}$, the entanglement wedge cross section, and the breakdown of the split property
• The Negativity Hamiltonian: An operator characterization of mixed-state entanglement
• Genus Two Partition Functions and Renyi Entropies of Large c CFTs
• Wormholes from heavy operator statistics in AdS/CFT
• Replica Wormholes and Holographic Entanglement Negativity
• Modular Flow as a Disentangler
• Holographic coherent states from random tensor networks
• Holographic Subregion Complexity for Singular Surfaces
• Islands for Entanglement Negativity
• Distinguishing Random and Black Hole Microstates
• Bulk entanglement entropy in perturbative excited states
• Fun with replicas: tripartitions in tensor networks and gravity
• Quantum algorithms for estimating quantum entropies
• Entanglement resolution of free Dirac fermions on a torus
• Exact Gravity Duals for Simple Quantum Circuits
• Page Curve for Entanglement Negativity through Geometric Evaporation
• Entanglement of Local Operators and the Butterfly Effect
• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Subsystem trace distance in low-lying states of $(1+1)$-dimensional conformal field theories
• Islands with Gravitating Baths: Towards ER = EPR
• Lattice study of Rényi entanglement entropy in $SU(N_c)$ lattice Yang-Mills theory with $N_c=2,3,4$
• Universality in the Shape Dependence of Holographic Rényi Entropy for General Higher Derivative Gravity
• Codimension-n Holography for Cones
• Towards classification of holographic multi-partite entanglement measures
• Einstein-AdS action, renormalized volume/area and holographic Renyi entropies
• Holographic Tensor Networks in Full AdS/CFT
• Mixed State Entanglement for Holographic Axion Model
• Barrier from chaos: operator entanglement dynamics of the reduced density matrix
• Island on codimension-two branes in AdS/dCFT
• Rényi and Tsallis entropies: three analytic examples
• Microcanonical Action and the Entropy of Hawking Radiation
• Rényi Topology of Charged-flat Black Hole: Hawking-Page and Van-der-Waals Phase Transitions
• Holographic Renyi Entropy at High Energy Density
• Approximate Bacon-Shor Code and Holography
• Rényi Mutual Information in Quantum Field Theory
• Rényi and Tsallis entropies of the Aharonov-Bohm ring in uniform magnetic fields
• Holographic second laws of black hole thermodynamics
• Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy
• Evolutions of entanglement and complexity after a thermal quench in massive gravity theory
• Capacity of Entanglement in Local Operators
• Looking at Shadows of Entanglement Wedges
• Topological terms, AdS_2n gravity and renormalized Entanglement Entropy of holographic CFTs
• Quantum corrections to finite radius holography and holographic entanglement entropy
• Note on ETH of descendant states in 2D CFT
• Gravity duals of boundary cones
• AdS/BCFT from Conformal Bootstrap: Construction of Gravity with Branes and Particles
• Aspects of Holographic Entanglement Entropy for $T\bar{T}$-deformed CFTs
• Gravitational back-reaction is magical
• Path Integrals for Causal Diamonds and the Covariant Entropy Principle
• Supersymmetric Rényi Entropy and Defect Operators
• Renormalization of Entanglement Entropy from topological terms
• The Effect of Anisotropy on Holographic Entanglement Entropy and Mutual Information
• Mixed State Entanglement and Thermal Phase Transitions
• Building Bulk Geometry from the Tensor Radon Transform
• Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement
• Shape dependence of renormalized holographic entanglement entropy
• Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
• All the entropies on the light-cone
• Thermal fluctuations of black holes with non-linear electrodynamics and charged Renyi entropy
• Effective Action, Spectrum and First Law of Wedge Holography
• Page curve from dynamical branes in JT gravity
• Geodesic string condensation from symmetric tensor gauge theory: a unifying framework of holographic toy models
• Virasoro Entanglement Berry Phases
• Renormalized holographic entanglement entropy for Quadratic Curvature Gravity
• Logarithmic, Fractal and Volume-Law Entanglement in a Kitaev chain with long-range hopping and pairing
• Rényi Mutual Information in Holographic Warped CFTs
• Monotonicity conjecture for multi-party entanglement I
• Entanglement Entropy for $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed holographic CFT
• Entanglement spectrum of geometric states
• Entanglement Wedge Minimum Cross-section in Holographic Massive Gravity Theory
• Post-Quantum Quench Growth of Renyi Entropies in Low Dimensional Continuum Bosonic Systems
• Holographic duality between local Hamiltonians from random tensor networks
• A Modified Cosmic Brane Proposal for Holographic Renyi Entropy
• Discrete Gravity on Random Tensor Network and Holographic Rényi Entropy
• Holographic Tensor Networks with Bulk Gauge Symmetries
• A generalization of the maximum entropy principle for curved statistical manifolds
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Real-time gravitational replicas: Low dimensional examples
• Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories
• Tensor network state correspondence and holography
• Covariant holographic negativity from the entanglement wedge in AdS${}_3/$CFT${}_2$
• Holographic Complexity of LST and Single Trace $T\bar{T}$
• Complexity growth in Gubser-Rocha models with momentum relaxation
• Interplay of entanglement structures and stabilizer entropy in spin models
• More on symmetry resolved operator entanglement
• Thermodynamics of exponential Kolmogorov-Nagumo averages
• Rényi entropies and area operator from gravity with Hayward term
• Ensemble Estimation of Generalized Mutual Information with Applications to Genomics
• What's the Point? Hole-ography in Poincare AdS
• Quantum error correction and entanglement spectrum in tensor networks
• Entanglement Wedge Minimum Cross-Section for Holographic Aether Gravity
• On minimal entanglement wedge cross section for holographic entanglement negativity
• Non-geometric States in a Holographic Conformal Field Theory
• The holographic dual of Rényi relative entropy
• Quantum hypothesis testing in many-body systems
• Thermalization of Randomly Coupled SYK Models
• Replica Trick Calculation for Entanglement Entropy of Static Black Hole Spacetimes
• Holographic Renyi entropies from hyperbolic black holes with scalar hair
• Mixed-state Entanglement for AdS Born-Infeld Theory
• Sum rule for the pseudo-Rényi entropy
• Pseudo entropy and pseudo-Hermiticity in quantum field theories
• Holographic Reflected Entropy and Islands in Interface CFTs
• Casimir Effect and Holographic Dual of Wedges
• Tensor chain and constraints in tensor networks
• $dS$ extremal surfaces, replicas, boundary Renyi entropies in $dS/CFT$ and time entanglement
• Non-analyticity of holographic Rényi entropy in Lovelock gravity
• Negative Complexity of Formation: the Compact Dimensions Strike Back
• 1+1D Hadrons Minimize their Biparton Renyi Free Energy
• Entanglement Negativity and Replica Symmetry Breaking in General Holographic States
• Wormholes with Ends of the World
• U(1) CS Theory vs SL(2) CS Formulation: Boundary Theory and Wilson Line
• Holographic Rényi entropy for two-dimensional $\mathcal{N}$=(2,2) superconformal field theory
• Pacman geometries and the Hayward term in JT gravity
• The entanglement entropy of typical pure states and replica wormholes
• Subsystem entropy in 2d CFT and KdV ETH
• Musings on SVD and pseudo entanglement entropies
• Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations
• Proof of Renyi QNEC for free fermions
• Entanglement Properties of SU(2) Gauge Theory
• Geometric Quantum Discord Signals Non-Factorization
• Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-$c$ CFT Ensemble
• Negative R$\acute{\text{e}}$nyi entropy and Brane intersection
• Rényi entropy at large energy density in 2D CFT
• Evolution of capacity of entanglement and modular entropy in harmonic chains and scalar fields
• Cone Holography with Neumann Boundary Conditions and Brane-localized Gauge Fields
• Thermodynamics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime
• A Tale of Two Saddles
• The area operator and fixed area states in conformal field theories
• The Complexity of Being Entangled
• Conical defects and holography in topological AdS gravity
• Localized thermal states and negative energy
• Holographic supersymmetric Renyi entropies from hyperbolic black holes with scalar hair
• Holographic Mutual Information of Two Disjoint Spheres
• Average scattering entropy for periodic, aperiodic and random distribution of vertices in simple quantum graphs
• Entanglement in conformal field theory and holography
• Classical Holographic Codes
• Gauge protected entanglement between gravity and matter
• Decoding general error correcting codes and the role of complementarity
• Twist operators and pseudo entropies in two-dimensional momentum space
• QCD, with Strings Attached
• Does connected wedge imply distillable entanglement?
• Entanglement Rényi entropies in celestial holography
• Gravity dualities of quantum distances
• Geometric Structures Induced by Deformations of the Legendre Transform
• Position and momentum operators for a moving particle in bulk
• Hyperfine Structure of Quantum Entanglement
• Holographic entanglement negativity for a single subsystem in conformal field theories with a conserved charge
• Geometric methods in quantum information and entanglement variational principle
• Reconstructing the boundary of AdS from an infrared defect
• Renyi reflected entropy and entanglement wedge cross section with cosmic branes in AdS/BCFT
• On the Rényi entropy of Lifshitz and hyperscaling violating black holes
• Noncommutative corrections to the minimal surface areas of the pure AdS spacetime and Schwarzschild-AdS black hole
• Correlations in geometric states
• Fluctuations and non-Gaussianity in de Sitter spacetime from holographic entanglement entropy
• Sublinear quantum algorithms for estimating von Neumann entropy
• The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity
• Holographic AME states in black hole interiors
• Position dependence of the holographic entanglement entropy for an accelerating quark-antiquark pair
• Probing the Factorized Island Branch with the Capacity of Entanglement in JT Gravity
• Holographic entanglement entropy of two disjoint intervals in AdS${}_3$/CFT${}_2$
• A universal approach to Renyi entropy of multiple disjoint intervals
• Rényi complexity in mean-field disordered systems
• Spectral Projections for Density Matrices in Quantum Field Theories