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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Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
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abstract
We propose that holographic entanglement entropy can be calculated at arbitrary orders in the bulk Planck constant using the concept of a "quantum extremal surface": a surface which extremizes the generalized entropy, i.e. the sum of area and bulk entanglement entropy. At leading order in bulk quantum corrections, our proposal agrees with the formula of Faulkner, Lewkowycz, and Maldacena, which was derived only at this order; beyond leading order corrections, the two conjectures diverge. Quantum extremal surfaces lie outside the causal domain of influence of the boundary region as well as its complement, and in some spacetimes there are barriers preventing them from entering certain regions. We comment on the implications for bulk reconstruction.
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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.
q-Askey deformations of double-scaled SYK yield transfer matrices for orthogonal polynomials whose semiclassical chord dynamics map to ER bridges and new geometric transitions in sine dilaton gravity.
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.
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.
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.
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.
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.
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.
Typical states in large-N holographic CFTs exhibit UV and IR length scales set by energy and charges, producing factorization that isolates black holes via a corona of saturated entanglement wedges and extends ETH to rotating ensembles.
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.
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.
Evanescent quantum extremal surfaces, bounded in area but not generalized entropy, diagnose failures of spacetime emergence in holography.
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.
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.
In JT gravity, the capacity of entanglement detects finite-n structure in the factorized island saddle that the entropy misses at first nontrivial order.
Semiclassical crossed product constructions extend the algebraic reconstruction theorem to type III algebras and yield an algebraic Ryu-Takayanagi formula for holographic duality.
A new action for entanglement entropy in AdS3/CFT2 derives gravity equations, reduces to a string worldsheet, reproduces bit threads, and unifies several quantum gravity conjectures.
In a doubly holographic black hole model, the dimension of the microstate Hilbert space equals the sum of the quantum-corrected thermodynamic entropies of the left and right black holes, which equals the generalised entropy quantifying entanglement between the asymptotic boundaries.
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.
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.
Review of classical energy conditions, their quantum violations, and information-theoretic bounds for semi-classical gravity, based on Modave lectures.
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.
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.
-
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.
-
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.
-
q-Askey Deformations of Double-Scaled SYK
q-Askey deformations of double-scaled SYK yield transfer matrices for orthogonal polynomials whose semiclassical chord dynamics map to ER bridges and new geometric transitions in sine dilaton gravity.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
Entanglement inequalities, black holes and the architecture of typical states
Typical states in large-N holographic CFTs exhibit UV and IR length scales set by energy and charges, producing factorization that isolates black holes via a corona of saturated entanglement wedges and extends ETH to rotating ensembles.
-
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.
-
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.
-
A Semiclassical Diagnostic for Spacetime Emergence
Evanescent quantum extremal surfaces, bounded in area but not generalized entropy, diagnose failures of spacetime emergence in holography.
-
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.
-
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.
-
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.
-
Semiclassical algebraic reconstruction for type III algebras
Semiclassical crossed product constructions extend the algebraic reconstruction theorem to type III algebras and yield an algebraic Ryu-Takayanagi formula for holographic duality.
-
Toward a worldsheet theory of entanglement entropy
A new action for entanglement entropy in AdS3/CFT2 derives gravity equations, reduces to a string worldsheet, reproduces bit threads, and unifies several quantum gravity conjectures.
-
Quantum corrected black hole microstates and entropy
In a doubly holographic black hole model, the dimension of the microstate Hilbert space equals the sum of the quantum-corrected thermodynamic entropies of the left and right black holes, which equals the generalised entropy quantifying entanglement between the asymptotic boundaries.
-
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.
-
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.
-
Modave lectures on energy conditions in quantum field theory and semi-classical gravity
Review of classical energy conditions, their quantum violations, and information-theoretic bounds for semi-classical gravity, based on Modave lectures.
-
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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Lectures on entanglement entropy in field theory and holography
Lecture notes surveying entanglement entropy in QFT and holography, emphasizing physical aspects and the Ryu-Takayanagi formula.
- Twirled Perfect Tensor Networks: Computationally covariant holographic tensor networks