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.
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.
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.
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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