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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Entanglement Wedge Reconstruction and the Information Paradox
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abstract
When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time $\beta/2\pi \log S_{BH}$ into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall. By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox.
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representative citing papers
Mellin averaging over N reproduces the ensemble-like randomness of wormhole physics in the gravitational path integral when the dual theory admits analytic continuation in N and observables fluctuate superpolynomially small in N.
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.
Topology change in canonical JT gravity resolves the firewall paradox by making the connected two-interior branch dominate after Page time, with gravitational constraints annihilating the firewall branch and identifying horizon vacuum and early radiation purity as the same Dirac observable.
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 JT gravity with an end-of-the-world brane, the renormalized interior length — read as subsystem complexity — grows linearly, peaks around the Page time, and then decays exponentially, with growing relative fluctuations afterward.
A new singularity theorem establishes that evaporating black holes in semiclassical gravity are singular under weaker causality assumptions and the Generalized Second Law.
Modular flow in SYK models coupled to a bath reveals singularities allowing reconstruction of bulk flow past the horizon in two-sided AdS2 black holes.
Non-orientable topological gravity produces a resummed topological expansion whose late-time behavior matches the GOE universality class of random matrix theory for time-reversal invariant chaotic systems.
Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
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.
In 2D centaur geometries the entropy difference of a modular-conjugate Hawking-pair probe traces an inverse mini-Page curve that bottoms at τ≈β/8, marking when information begins to leave the cosmological horizon.
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.
Derives closed expressions for power moments of entanglement entropy of random states via Schur-Weyl duality and S_N character theory.
The paper proposes a kinematic space for any subregion of vacuum AdS, whose geodesic 'PEE threads' uniformly cover the subregion and yield tensor-network models that reproduce Ryu-Takayanagi entropy and realize surface/state and generalized-wedge 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.
Hawking radiation of a large black hole terminates near the scrambling time under SFT-style nonlocal smearing, producing a macroscopic remnant instead of complete evaporation.
When the RT area is O(1/G) and bulk entropy O(1), CCKLP-style reconstruction errors are exponentially small in G relative to area-function corrections.
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.
Fuzzball models with stretched horizons modify or eliminate entanglement islands depending on boundary conditions and cap geometry, producing information paradox analogues in some cases.
Inner horizon saddles supply the semiclassical correction -exp(A_inner/4G) to near-extremal black-hole entropy and motivate a spectral KSW criterion for well-defined one-loop effects around complex gravitational saddles.
Evanescent quantum extremal surfaces, bounded in area but not generalized entropy, diagnose failures of spacetime emergence in holography.
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.
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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Wormholes and Averaging over N
Mellin averaging over N reproduces the ensemble-like randomness of wormhole physics in the gravitational path integral when the dual theory admits analytic continuation in N and observables fluctuate superpolynomially small in N.
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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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Smooth horizons from topology change in canonical quantum gravity
Topology change in canonical JT gravity resolves the firewall paradox by making the connected two-interior branch dominate after Page time, with gravitational constraints annihilating the firewall branch and identifying horizon vacuum and early radiation purity as the same Dirac observable.
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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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Evaporating Black Hole Interior and Complexity Evolution
In JT gravity with an end-of-the-world brane, the renormalized interior length — read as subsystem complexity — grows linearly, peaks around the Page time, and then decays exponentially, with growing relative fluctuations afterward.
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A Quantum Singularity Theorem for the Evaporating Black Hole
A new singularity theorem establishes that evaporating black holes in semiclassical gravity are singular under weaker causality assumptions and the Generalized Second Law.
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Probing Evaporating Black Holes with Modular Flow in SYK
Modular flow in SYK models coupled to a bath reveals singularities allowing reconstruction of bulk flow past the horizon in two-sided AdS2 black holes.
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Mind the crosscap: $\tau$-scaling in non-orientable gravity and time-reversal-invariant systems
Non-orientable topological gravity produces a resummed topological expansion whose late-time behavior matches the GOE universality class of random matrix theory for time-reversal invariant chaotic systems.
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Living on the edge: a non-perturbative resolution to the negativity of bulk entropies
Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
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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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The mini-Page Curve in Cosmology
In 2D centaur geometries the entropy difference of a modular-conjugate Hawking-pair probe traces an inverse mini-Page curve that bottoms at τ≈β/8, marking when information begins to leave the cosmological horizon.
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Wormholes as red herrings: reflection positivity and the reconstruction of unitary quantum field theories
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.
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Revisiting the Page curve and its moments. A combinatorial approach
Derives closed expressions for power moments of entanglement entropy of random states via Schur-Weyl duality and S_N character theory.
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Holography and Kinematic Space for Gravitational Sub-regions in AdS
The paper proposes a kinematic space for any subregion of vacuum AdS, whose geodesic 'PEE threads' uniformly cover the subregion and yield tensor-network models that reproduce Ryu-Takayanagi entropy and realize surface/state and generalized-wedge holography.
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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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Macroscopic Black-Hole Remnants in a Nonlocal Field Theory: Towards Hawking Radiation in SFT
Hawking radiation of a large black hole terminates near the scrambling time under SFT-style nonlocal smearing, producing a macroscopic remnant instead of complete evaporation.
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A Note on Corrections to Entanglement Wedge Reconstruction
When the RT area is O(1/G) and bulk entropy O(1), CCKLP-style reconstruction errors are exponentially small in G relative to area-function corrections.
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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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Entanglement islands, fuzzballs and stretched horizons
Fuzzball models with stretched horizons modify or eliminate entanglement islands depending on boundary conditions and cap geometry, producing information paradox analogues in some cases.
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Inner Horizon Saddles and a Spectral KSW Criterion
Inner horizon saddles supply the semiclassical correction -exp(A_inner/4G) to near-extremal black-hole entropy and motivate a spectral KSW criterion for well-defined one-loop effects around complex gravitational saddles.
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A Semiclassical Diagnostic for Spacetime Emergence
Evanescent quantum extremal surfaces, bounded in area but not generalized entropy, diagnose failures of spacetime emergence in holography.
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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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Entropy bound and the non-universality of entanglement islands
Universal compact entanglement islands are obstructed by an entropy bound violation, implying region-dependent interior reconstruction.
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Probing the Factorized Island Branch with the Capacity of Entanglement in JT Gravity
In JT gravity, the capacity of entanglement detects finite-n structure in the factorized island saddle that the entropy misses at first nontrivial order.
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Single-Sided Black Holes in Double-Scaled SYK Model and No Man's Island
In the double-scaled SYK model with an end-of-the-world brane, the boundary algebra for a single-sided black hole is a type II1 von Neumann factor with non-trivial commutant, preventing full bulk reconstruction and creating a no man's island behind the horizon.
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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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Covariant phase space and the semi-classical Einstein equation
A semi-classical symplectic two-form is defined as the sum of the gravitational symplectic form and the Berry curvature of the quantum matter state; it is shown to be independent of the Cauchy slice and to satisfy a quantum generalization of the Hollands-Iyer-Wald identity.
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The Remnant of an Evaporating Rotating Regular Black Hole from the Generalized Entropy in the Final Stage of Evaporation
A rotating regular black hole leaves a remnant because the correction term in the generalized entropy of Hawking radiation vanishes at a finite mass above the extremal limit.
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On Integrable Structures on Non-compact Boundaries in Three-Dimensional Gravity
In the diagonal (Cartan) sector of AdS3 gravity, the radial flow of the quasi-local stress tensor satisfies an exact T Tbar-like equation, while the boundary time evolution forms an integrable bi-Hamiltonian hierarchy.
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On Black Holes Surrounded by Radiation II: Thermodynamics
Hillingar black holes thermodynamically mimic ordinary black holes of mass M, sharing temperature and entropy under thermal equilibrium.
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Modular quantization and black holes
Modular quantization of a single holographic CFT reproduces exact Hartle-Hawking correlators of smooth BTZ black holes in the semiclassical limit while yielding non-smooth stretched-horizon descriptions at finite GN.
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Asymptotic Algebras and Holography of Information in CGHS Model
Establishes holography of information in the CGHS model via asymptotic algebras and argues that islands violate commutativity of left- and right-boundary algebras.
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The fate of Reissner--Nordstr\"om--de Sitter black holes: nonequilibrium discharge and evaporation
Semiclassical RN-dS evaporation via 2D dilaton gravity and anomaly flux yields monotonic neutral mass loss and rapid discharge, making classical equilibrium loci non-attractors and leading to empty de Sitter space.
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A Timelike Quantum Focusing Conjecture
A timelike quantum focusing conjecture implies a complexity-based quantum strong energy condition and a complexity bound analogous to the covariant entropy bound for suitable codimension-0 field theory complexity measures.
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Generalized Entanglement Wedges and the Connected Wedge Theorem
Generalized entanglement wedges rephrase the connected wedge theorem in bulk entropy terms, yielding mutual information bounds and a scattering-to-connected-wedge implication that extends to flat spacetimes.
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Memory-Burden Suppression of Hawking Radiation and Neutrino Constraints on Primordial Black Holes
Memory-burden backreaction deforms the Hawking spectrum to suppress its high-energy tail, lowering total luminosity and neutrino flux by a factor set by a single suppression parameter and thereby relaxing IceCube bounds on primordial black hole dark matter.
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UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox
Hawking radiation terminates around the scrambling time due to trans-Planckian stringy effects in GUP and string-field-theory-inspired toy models, yielding negligible evaporation and a mostly classical black hole.
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Imprints of dynamical phases in semiclassical entanglement entropy in 2D CFT
Semiclassical entanglement entropy in driven 2D CFT states exhibits dynamical phase imprints; the holographic backreacted minimal area matches the CFT result at O(c^0) and verifies the FLM conjecture.
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Rethinking quantum information in gravity and fields
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.
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Lecture notes on strings in AdS$_3$ from the worldsheet and the AdS$_3$/CFT$_2$ duality
Lecture notes deliver a self-contained pedagogical overview of worldsheet strings in AdS3 with NSNS flux, summarizing 25 years of results with emphasis on spectrally flowed correlation functions.
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