Replica wormhole geometries justify the replica trick computation of the Page curve in holographic black hole models and support entanglement wedge reconstruction via the Petz map.
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Holographic Derivation of Entanglement Entropy from AdS/CFT
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abstract
A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from AdS/CFT correspondence. We argue that the entanglement entropy in d+1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS_{d+2}, analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal perfectly reproduces the correct entanglement entropy in 2D CFT when applied to AdS_3. We also compare the entropy computed in AdS_5 \times S^5 with that of the free N=4 super Yang-Mills.
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representative citing papers
Reinforcement learning finds explicit graph realizations for three of six previously unresolved extreme rays of the N=6 holographic entropy cone and supplies evidence that the other three lie outside it.
Replica wormholes in the gravitational path integral yield the island rule for the fine-grained entropy of Hawking radiation, ensuring it follows the unitary Page curve in two-dimensional dilaton gravity.
Hawking radiation entropy follows the Page curve when quantum extremal surfaces are identified with RT/HRT surfaces in a higher-dimensional holographic dual, making the black hole interior part of the radiation's entanglement wedge.
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
For n=2, Rényi multi-entropies in RTNs are determined by minimal multiway cuts; the minimal multiway cut conjecture fails for integer n>2 with explicit counterexamples.
A unitary defect CFT at the wedge corner supplies an auxiliary holographic entropy term that balances area variations and enables stable non-horizon islands in massless ghost-free wedge holography.
In large-central-charge holographic CFTs, post-quench mutual information organizes into six phases governed by conformal block dominance and D4 symmetry breaking to Z2 x Z2.
Twirled perfect tensor networks achieve computational covariance, bound complexity by the PLC, and obey a lattice Ryu-Takayanagi formula for arbitrary boundary subregions.
q-Askey deformations of DSSYK produce transfer matrices from basic orthogonal polynomials whose chord numbers map to ER bridge lengths and signal geometric transitions with discrete spectra in sine dilaton gravity.
Mini-boson stars in AdS spacetime are proposed as holographic realizations of quantum scars, exhibiting chaotic spectra with integrable subsectors, anomalously low entanglement, and robust Krylov complexity revivals.
Higher spin gravity path integral on S^4 glues to an Sp(N) or superconformal S^3 boundary theory, giving leading contribution 2^N with one-loop cancellations.
In the continuum limit the discrete Krylov chain becomes a Klein-Gordon field in AdS2, with Lanczos growth rate α identified as πT, recovering the maximal chaos bound and requiring the Breitenlohner-Freedman bound for consistency.
Generalized entanglement entropies are constructed via left-, right-, and bi-invariant unit-invariant singular value decompositions to ensure scale invariance for non-Hermitian and rectangular operators in quantum mechanics, random matrices, and Chern-Simons theory.
Bulk single-particle states of a massive Chern-Simons vector in AdS3 produce entanglement entropy corrections that match the CFT replica-trick result for the corresponding primary and descendants at leading and sub-leading orders, with vanishing edge-mode contribution.
An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.
Subregion duality fails in AdS/CFT at leading large N, leading to the proposal of subregion complementarity allowing different CFT operators to describe one bulk subregion.
In a 2d evaporating black hole model, large boosts create O(1/G_N) gradients in bulk entropy that move the quantum extremal surface, causing the generalized entropy to follow unitary expectations with information disappearing after a scrambling time and a phase transition at the Page time.
MERA tensor networks produce continuously varying effective scaling dimensions along the Z3 chiral clock critical line, starting from 3-state Potts values as the chiral parameter increases.
A single-band lattice model on the BTZ cylinder produces a curvature-dependent Harper equation whose spectra show sharpened butterfly fragmentation at weak curvature and suppressed magnetic response near larger horizons.
Multi-entropy exhibits a structural obstruction to replica symmetry breaking in random tensor networks due to incompatible boundary permutations in the replica hypercube, unlike entanglement negativity.
Krylov complexity grows quadratically in pure Lifshitz backgrounds and its late-time exponent is controlled by the hyperscaling violation parameter, with a special oscillatory regime.
Entanglement entropies in 2d holographic CFTs are rewritten via crossing symmetry as algebraic Virasoro entropies whose O(c) piece is identified with the RT area through saddle-dominated Cardy density after coarse-graining heavy primaries into Liouville-momentum bins.
Two sets of holographic tensor network rules from independent papers are shown to be equivalent, connecting observer inclusion with generalized entanglement wedge proposals.
citing papers explorer
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Replica wormholes and the black hole interior
Replica wormhole geometries justify the replica trick computation of the Page curve in holographic black hole models and support entanglement wedge reconstruction via the Petz map.
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Exploring the holographic entropy cone via reinforcement learning
Reinforcement learning finds explicit graph realizations for three of six previously unresolved extreme rays of the N=6 holographic entropy cone and supplies evidence that the other three lie outside it.
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Replica Wormholes and the Entropy of Hawking Radiation
Replica wormholes in the gravitational path integral yield the island rule for the fine-grained entropy of Hawking radiation, ensuring it follows the unitary Page curve in two-dimensional dilaton gravity.
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The Page curve of Hawking radiation from semiclassical geometry
Hawking radiation entropy follows the Page curve when quantum extremal surfaces are identified with RT/HRT surfaces in a higher-dimensional holographic dual, making the black hole interior part of the radiation's entanglement wedge.
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Complexity Inequalities for Quantum Subsystems
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
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Multi-entropy in random tensor networks
For n=2, Rényi multi-entropies in RTNs are determined by minimal multiway cuts; the minimal multiway cut conjecture fails for integer n>2 with explicit counterexamples.
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Massless Islands in Wedge Holography
A unitary defect CFT at the wedge corner supplies an auxiliary holographic entropy term that balances area variations and enables stable non-horizon islands in massless ghost-free wedge holography.
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Dynamical Entanglement Phase Transitions in Holographic CFTs
In large-central-charge holographic CFTs, post-quench mutual information organizes into six phases governed by conformal block dominance and D4 symmetry breaking to Z2 x Z2.
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Twirled Perfect Tensor Networks: Computationally covariant holographic tensor networks
Twirled perfect tensor networks achieve computational covariance, bound complexity by the PLC, and obey a lattice Ryu-Takayanagi formula for arbitrary boundary subregions.
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q-Askey Deformations of Double-Scaled SYK
q-Askey deformations of DSSYK produce transfer matrices from basic orthogonal polynomials whose chord numbers map to ER bridge lengths and signal geometric transitions with discrete spectra in sine dilaton gravity.
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Quantum scars from holographic boson stars
Mini-boson stars in AdS spacetime are proposed as holographic realizations of quantum scars, exhibiting chaotic spectra with integrable subsectors, anomalously low entanglement, and robust Krylov complexity revivals.
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dS$^4$ Metamorphosis
Higher spin gravity path integral on S^4 glues to an Sp(N) or superconformal S^3 boundary theory, giving leading contribution 2^N with one-loop cancellations.
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Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography
In the continuum limit the discrete Krylov chain becomes a Klein-Gordon field in AdS2, with Lanczos growth rate α identified as πT, recovering the maximal chaos bound and requiring the Breitenlohner-Freedman bound for consistency.
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Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition
Generalized entanglement entropies are constructed via left-, right-, and bi-invariant unit-invariant singular value decompositions to ensure scale invariance for non-Hermitian and rectangular operators in quantum mechanics, random matrices, and Chern-Simons theory.
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Precision tests of bulk entanglement: $AdS_3$ vectors
Bulk single-particle states of a massive Chern-Simons vector in AdS3 produce entanglement entropy corrections that match the CFT replica-trick result for the corresponding primary and descendants at leading and sub-leading orders, with vanishing edge-mode contribution.
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Symmetry-Resolved Entanglement Entropy from Heat Kernels
An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.
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Subregion Complementarity in AdS/CFT
Subregion duality fails in AdS/CFT at leading large N, leading to the proposal of subregion complementarity allowing different CFT operators to describe one bulk subregion.
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The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
In a 2d evaporating black hole model, large boosts create O(1/G_N) gradients in bulk entropy that move the quantum extremal surface, causing the generalized entropy to follow unitary expectations with information disappearing after a scrambling time and a phase transition at the Page time.
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Scaling at Chiral Clock Criticality via Entanglement Renormalization
MERA tensor networks produce continuously varying effective scaling dimensions along the Z3 chiral clock critical line, starting from 3-state Potts values as the chiral parameter increases.
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Hofstadter's Butterfly in AdS$_3$ Black Holes
A single-band lattice model on the BTZ cylinder produces a curvature-dependent Harper equation whose spectra show sharpened butterfly fragmentation at weak curvature and suppressed magnetic response near larger horizons.
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Structural Obstruction to Replica Symmetry Breaking for Multi-Entropy in Random Tensor Networks
Multi-entropy exhibits a structural obstruction to replica symmetry breaking in random tensor networks due to incompatible boundary permutations in the replica hypercube, unlike entanglement negativity.
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Holographic Krylov Complexity with Lifshitz Scaling and Hyperscaling Violation
Krylov complexity grows quadratically in pure Lifshitz backgrounds and its late-time exponent is controlled by the hyperscaling violation parameter, with a special oscillatory regime.
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Ryu-Takayanagi area from Virasoro modular data
Entanglement entropies in 2d holographic CFTs are rewritten via crossing symmetry as algebraic Virasoro entropies whose O(c) piece is identified with the RT area through saddle-dominated Cardy density after coarse-graining heavy primaries into Liouville-momentum bins.
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Subregion observer rules from generalized entanglement wedges
Two sets of holographic tensor network rules from independent papers are shown to be equivalent, connecting observer inclusion with generalized entanglement wedge proposals.
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Quantum Black Hole Chemistry from Double Holography
In double holography, quantum backreaction from cutoff matter on a physical brane supplies a distinct color variable, resolving color-volume degeneracy for the quantum BTZ black hole.
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Real-time pseudo entropy and modular-Hamiltonian correlations
Short-time real-time pseudo entropy obeys S_A(t,0)=S_A(0)-it ⟨K_A(H−⟨H⟩)⟩ + O(t²), with imaginary response from symmetrized covariance of H and K_A.
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Pure states for subregions in gravity and their entanglement entropy
A construction assigns pure states to subregions in quantum gravity via partially frozen path integrals and gives a holographic prescription for their entanglement entropy that satisfies consistency conditions and recovers known formulas.
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Quantum State of a Gravitating Region
Proposal that compact d-manifolds with elliptic data prepare boundary quantum states |J>, with Rényi entropies from path integrals agreeing with minimal-surface formulas after analytic continuation.
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Exact Bulk-Boundary Pairs in AdS/CFT
Exact pairing of CFT two-point functions with interior AdS geodesics on open solid torus via conformal kinematics, without semiclassical approximations.
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Gauging Time Reversal Symmetry in Quantum Gravity: Arrow of Time from a Confinement--Deconfinement Transition
The emergence of the cosmological arrow of time is identified with a confinement-deconfinement transition in a Z2 lattice gauge theory on LQG spin networks, with the deconfined phase corresponding to a CZX-type SPT phase.
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GR from RG: Gravity Is Induced From Renormalization Group Flow In The Infrared
Holographic RG flow induces gravity by evolving boundary conditions from rigid Dirichlet to mixed Dirichlet-Neumann, generating an Einstein-Hilbert term and evading the Weinberg-Witten theorem.
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Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography
Deformations of the double-scaled SYK model via finite-cutoff holography produce Krylov complexity as wormhole length and realize Susskind's stretched horizon proposal through targeted T² deformations in the high-energy spectrum.
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Holographic Tensor Networks as Tessellations of Geometry
Holographic tensor networks constructed from PEE-thread tessellations of AdS geometry reproduce the exact Ryu-Takayanagi formula in factorized EPR, perfect-tensor, and random variants.
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Modular Witten Diagrams and Quantum Extremality
Modular Witten diagrams reproduce the O(λ² G_N) correction to holographic entanglement entropy, matching the canonical energy term in the quantum Ryu-Takayanagi formula with wedge shape deformation.
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(Iso)spin from Isospin in Top-Down Holography
In top-down holographic models, monopole-induced diagonal symmetry causes dilaton fluctuations to mix SU(2) gauge and SO(3) isometry angular momenta, reproducing the Jackiw-Rebbi-Hasenfratz-'t Hooft spin-from-isospin mechanism.
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Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity
Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specific regions while depending on Krylov complexity of the Hartle-Hawking state.
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Curious QNEIs from QNEC: New Bounds on Null Energy in Quantum Field Theory
Derives new state-independent lower bounds on semi-local integrals of null energy flux in QFTs of two and higher dimensions using QNEC, strong subadditivity, and modular Hamiltonians.
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Conformal Blocks in 2d Carrollian/Galilean CFTs and Excited State Entanglement Entropy
Derives heavy-light conformal blocks in 2d C/G CFTs and computes excited-state entanglement entropy via replica trick, finding thermal form that reproduces holographic EE and establishes dictionary between boundary weights and bulk mass/angular momentum.
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Quantum Bit Threads and the Entropohedron
Derives several new quantum bit thread prescriptions equivalent to quantum extremal surfaces for static holographic states and introduces entanglement distribution functions organized into the entropohedron convex polytope.
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Searching for emergent spacetime in spin glasses
Spectral functions of SYK, p-spin, and SU(M) Heisenberg models show exponential tails in spin-glass phases and quasiparticle families in spin-liquid phases, with a proof that exponential decay blocks detection of bulk causal structure.
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Entanglement spreading and emergent locality in Brownian SYK chains
In a Brownian SYK chain at strong coupling, information from an injected qudit spreads inside a sharp light-cone at the butterfly velocity because the governing dynamics reduce to FKPP domain walls.
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Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes
Minimal edge modes compatible with Chern-Simons topological invariance are proposed as quantum group particles, yielding a factorization of 3d gravity state space that matches proposals linking Bekenstein-Hawking entropy to topological entanglement entropy.
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Crosscap Quenches and Entanglement Evolution
Introduces crosscap quenches in CFTs and holographic models to derive universal entanglement entropy evolution, validated by numerics in spin systems.
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Entanglement Harvesting and Quantum Discord of Alpha Vacua in de Sitter Space
The reduced states of static UDW detectors coupled to a scalar field in alpha-vacua are derived analytically, revealing distinct behaviors of entanglement harvesting for time-like versus space-like separations and superhorizon suppression of quantum discord.
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Entropy Variations and Light Ray Operators from Replica Defects
Replica analysis shows QNEC saturation in interacting CFTs with twist gap because only the stress-tensor defect operator produces the contact term in the n to 1 limit.
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The nonlocal magic of a holographic Schwinger pair
Holographic Schwinger pair creation generates nonlocal magic for spacetime dimensions d>2, as shown by a non-flat entanglement spectrum that can be read from the probe brane free energy.
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Covariant Locally Localized Gravity and vDVZ Continuity
In the Karch-Randall braneworld the zero-graviton-mass limit of the one-loop partition function is a massless graviton plus a decoupled massive vector, not the pure Randall-Sundrum II model.
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Large-c BCFT Entanglement Entropy with Deformed Boundaries from Emergent JT Gravity
At large central charge, BCFT von Neumann entropy with deformed boundaries is reproduced by island entropy in an emergent JT gravity setup with transparent boundary conditions set by the deformation.
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The yes boundaries wavefunctions of the universe
Using two timelike boundaries and a nearly maximally entangled thermofield double state from dressed de Sitter Hamiltonian theories, the authors construct wavefunctions for extended cosmological spacetimes that include the future wedge and resolve entanglement entropy issues via 3D constrained path
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Holographic entanglement entropy, Wilson loops, and neural networks
Neural networks reconstruct both spatial and timelike bulk metric components from strip entanglement entropy and Wilson loops with sub-0.2% accuracy in holographic models such as AdS-Schwarzschild and Gubser-Rocha.