pith. machine review for the scientific record.
sign in

arxiv: 1911.12333 · v2 · pith:ARMV66U4new · submitted 2019-11-27 · ✦ hep-th

Replica Wormholes and the Entropy of Hawking Radiation

Ahmed Almheiri , Thomas Hartman , Juan Maldacena , Edgar Shaghoulian , Amirhossein Tajdini This is my paper

Pith reviewed 2026-05-18 18:58 UTC · model grok-4.3

classification ✦ hep-th
keywords replica wormholesblack hole information paradoxisland ruleHawking radiation entropyJT gravitygravitational path integralfine-grained entropy
0
0 comments X

The pith

Replica wormholes in the gravitational path integral lead to the island rule for Hawking radiation entropy, resolving the information paradox.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tries to establish that the information paradox for Hawking radiation can be resolved within semiclassical gravity by accounting for replica wormhole saddles in the path integral. Using the replica trick to compute entropy, these wormholes connect different copies of the black hole spacetime. Taking the limit to one replica produces the island rule, which gives the proper fine-grained entropy that follows the Page curve. A reader would care because this shows a concrete way for quantum information to be consistent with gravitational calculations without losing unitarity. The construction is carried out in two-dimensional Jackiw-Teitelboim gravity.

Core claim

The paper claims that new saddles corresponding to replica wormholes appear in the gravitational path integral when computing the entropy of Hawking radiation using replicas. As the replica number n approaches 1, these saddles lead to the island rule for the fine-grained gravitational entropy, fixing the large discrepancy with the original Hawking calculation and ensuring consistency with unitarity in the AdS to Minkowski setup.

What carries the argument

Replica wormhole saddles that connect the different copies in the replicated geometry and dominate the path integral contribution to the entropy.

If this is right

  • The von Neumann entropy of the Hawking radiation follows the island formula.
  • The entropy reaches a maximum and then decreases, matching unitary expectations.
  • This mechanism is demonstrated explicitly in JT gravity coupled to matter.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If true, this could extend to calculations of entanglement entropy in other spacetimes where wormholes might contribute.
  • Testable extensions include checking if similar saddles appear in higher-dimensional models or string theory embeddings.

Load-bearing premise

The semiclassical gravitational path integral is dominated by replica wormhole saddles when computing the von Neumann entropy via the replica trick, allowing analytic continuation to n near 1.

What would settle it

Computing the partition function or entropy in the JT gravity model and finding that other configurations dominate over the replica wormholes, leading to a different entropy formula, would falsify the claim.

read the original abstract

The information paradox can be realized in anti-de Sitter spacetime joined to a Minkowski region. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirements of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as complexified wormholes connecting different copies of the black hole. As the replica number $n \to 1$, the presence of these wormholes leads to the island rule for the computation of the fine-grained gravitational entropy. We discuss these replica wormholes explicitly in two-dimensional Jackiw-Teitelboim gravity coupled to matter.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that replica wormhole saddles in the gravitational path integral resolve the black hole information paradox by reconciling Hawking's von Neumann entropy of radiation with unitarity. In AdS spacetime joined to Minkowski, these complexified wormholes connecting replica copies yield the island rule for fine-grained entropy as the replica number n approaches 1. The derivation is carried out explicitly in two-dimensional JT gravity coupled to matter.

Significance. If the central result holds, the work supplies an explicit path-integral derivation of the island formula in a controlled semiclassical setting. Credit is given for the concrete identification of wormhole saddles and their on-shell actions in the JT model, which permits direct comparison with the disconnected replica contribution and furnishes a falsifiable gravitational mechanism for the Page curve.

major comments (2)
  1. [§4] §4 (replica wormhole saddles): the claim that these saddles dominate the path integral for integer n>1 rests on action comparison, yet the manuscript provides no quantitative bound on the contribution of alternate topologies or disconnected configurations; without this, the analytic continuation to n=1 that produces the island rule remains an assumption rather than a controlled limit.
  2. [replica method discussion] Discussion of the replica trick near n=1: the validity of the semiclassical approximation when continuing the entropy from integer n to n=1 is asserted but not bounded; if subleading saddles become comparable in this regime, the entropy reverts to the Hawking result and the island rule does not follow.
minor comments (2)
  1. [JT gravity section] Notation for the matter sector and dilaton boundary conditions could be stated more explicitly in the JT gravity setup to facilitate reproduction of the on-shell action.
  2. Figure captions would benefit from additional labels indicating which curves correspond to the wormhole versus disconnected contributions.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address each major comment below, providing clarifications on the dominance of saddles and the replica continuation. Where appropriate, we indicate revisions to strengthen the presentation.

read point-by-point responses

  1. Referee: [§4] §4 (replica wormhole saddles): the claim that these saddles dominate the path integral for integer n>1 rests on action comparison, yet the manuscript provides no quantitative bound on the contribution of alternate topologies or disconnected configurations; without this, the analytic continuation to n=1 that produces the island rule remains an assumption rather than a controlled limit.

    Authors: In response to this comment, we note that our analysis in §4 focuses on the two primary contributions: the connected replica wormhole and the disconnected replica geometries. We compute their on-shell actions explicitly in JT gravity and demonstrate that the wormhole saddle has a lower action for n > 1 in the relevant parameter regime, leading to its dominance. While we do not provide a quantitative bound encompassing every conceivable topology in the full path integral—which would indeed require a more advanced non-perturbative analysis—we argue that in the semiclassical limit, contributions from other topologies are suppressed. We will revise the manuscript to include additional discussion clarifying this point and the justification for focusing on these saddles. revision: partial

  2. Referee: [replica method discussion] Discussion of the replica trick near n=1: the validity of the semiclassical approximation when continuing the entropy from integer n to n=1 is asserted but not bounded; if subleading saddles become comparable in this regime, the entropy reverts to the Hawking result and the island rule does not follow.

    Authors: We appreciate this concern regarding the analytic continuation. The replica method requires evaluating the partition function for integer n and then continuing to n=1. In our work, the semiclassical saddles are identified for integer n, and their actions are continued analytically. The island rule emerges from the n→1 limit of the dominant saddle. We acknowledge that a strict error bound on the semiclassical approximation during continuation is not derived, as this would necessitate controlling all subleading effects uniformly. Nevertheless, the approach is consistent with standard uses of the replica trick in holographic settings, and the result reproduces the expected Page curve. We will add text to the manuscript discussing the assumptions underlying the continuation and the regime where the approximation holds. revision: partial

standing simulated objections not resolved
  • A fully quantitative bound over all possible topologies and a rigorous error bound for the analytic continuation in the semiclassical regime.

Circularity Check

0 steps flagged

No significant circularity in replica wormhole derivation of island rule

full rationale

The paper computes the replicated partition function in JT gravity by identifying and evaluating new wormhole saddle points that connect the replicas, then applies the standard replica trick formula for von Neumann entropy and takes the n→1 limit to obtain the island rule. This follows from direct evaluation of the on-shell gravitational action for the wormhole configurations rather than from any fitted parameter, self-referential definition, or load-bearing self-citation that presupposes the final result. The derivation remains self-contained within the semiclassical path integral of the model, with the dominance of these saddles justified by comparison of actions in the JT setup; external benchmarks such as the replica trick and JT gravity equations are independently established and do not incorporate the target island formula by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the applicability of the replica trick to gravitational path integrals and the dominance of wormhole saddles in the semiclassical limit; no free parameters are fitted to data, and the wormholes are derived rather than postulated ad hoc.

axioms (2)
  • domain assumption The replica trick applies to the computation of von Neumann entropy in gravitational systems via the path integral
    Invoked when introducing n copies and taking n to 1 to obtain the entropy formula.
  • domain assumption Semiclassical saddle-point approximation captures the dominant contributions to the gravitational path integral for the entropy
    Used to identify the replica wormholes as the relevant saddles.
invented entities (1)
  • replica wormholes no independent evidence
    purpose: Complexified gravitational saddles connecting different replica copies that contribute to the entropy path integral
    Derived as new saddle points in the replica manifold; no independent falsifiable evidence outside the calculation is provided.

pith-pipeline@v0.9.0 · 5643 in / 1591 out tokens · 39995 ms · 2026-05-18T18:58:53.551347+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 21 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Replica wormholes and the black hole interior

    hep-th 2019-11 conditional novelty 9.0

    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.

  2. Wormholes and Averaging over N

    hep-th 2026-05 unverdicted novelty 8.0

    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...

  3. Entanglement Wedge Reconstruction and the Information Paradox

    hep-th 2019-05 unverdicted novelty 8.0

    A phase transition in the quantum RT surface at the Page time derives the Page curve and enables entanglement wedge reconstruction of the black hole interior from Hawking radiation.

  4. Entanglement Revivals and Scrambling for Evaporating Black Holes

    hep-th 2026-04 unverdicted novelty 7.0

    Increasing black hole scrambling time in JT and RST evaporating geometries suppresses and eliminates late-time entanglement revivals in 2d CFT mutual information for disjoint intervals, interpolating between quasipart...

  5. Probing Evaporating Black Holes with Modular Flow in SYK

    hep-th 2025-12 unverdicted novelty 7.0

    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.

  6. Living on the edge: a non-perturbative resolution to the negativity of bulk entropies

    hep-th 2025-09 unverdicted novelty 7.0

    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.

  7. Entanglement islands, fuzzballs and stretched horizons

    hep-th 2026-05 unverdicted novelty 6.0

    Fuzzball models with stretched horizons modify or eliminate entanglement islands depending on boundary conditions and cap geometry, producing information paradox analogues in some cases.

  8. Wormholes and the imaginary distance bound

    hep-th 2026-05 unverdicted novelty 6.0

    Wormhole effects in theories with imaginary massless scalars set an upper limit on analytic continuation of couplings to imaginary values, with string theory examples showing the low-energy theory breaks down at or be...

  9. The nonlocal magic of a holographic Schwinger pair

    hep-th 2026-05 unverdicted novelty 6.0

    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.

  10. Entanglement Revivals and Scrambling for Evaporating Black Holes

    hep-th 2026-04 unverdicted novelty 6.0

    Black hole scrambling suppresses and eventually eliminates late-time entanglement revivals in CFT mutual information for disjoint intervals, with spikes vanishing when interval lengths become exponential in the scramb...

  11. State counting in gravity and maximal entropy principle

    hep-th 2026-04 unverdicted novelty 6.0

    The Bekenstein-Hawking entropy state counting and the Page curve for Hawking radiation entanglement entropy are equivalent from the gravity path integral viewpoint via a convex optimization problem for von Neumann entropy.

  12. Probing the Factorized Island Branch with the Capacity of Entanglement in JT Gravity

    hep-th 2026-04 unverdicted novelty 6.0

    In JT gravity, the capacity of entanglement detects finite-n structure in the factorized island saddle that the entropy misses at first nontrivial order.

  13. Kerr Black Hole Ringdown in Effective Field Theory

    gr-qc 2026-03 unverdicted novelty 6.0

    Effective field theory yields model-independent corrections to Kerr black hole quasinormal modes that oscillate logarithmically near extremality, indicating discrete scale invariance.

  14. Menagerie of Euclidean constructions for 3D holographic cosmologies

    hep-th 2026-01 unverdicted novelty 6.0

    Generalized Euclidean wormhole constructions in 3D gravity produce holographic duals to approximately homogeneous closed baby-universe cosmologies and identify a necessary condition for the cosmological saddle to domi...

  15. Single-Sided Black Holes in Double-Scaled SYK Model and No Man's Island

    hep-th 2025-11 unverdicted novelty 6.0

    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 cr...

  16. Albertian Channel Memory in Black-Hole Evaporation

    hep-th 2026-05 unverdicted novelty 5.0

    Black hole evaporation yields ordinary radiation carrying exceptional algebraic memory from the Albert algebra structure, reconstructing the Page curve without AMPS tensor factorization.

  17. How to have your wormholes and factorize, too

    hep-th 2026-02 unverdicted novelty 5.0

    A modified semiclassical holographic dictionary is used to construct an extended gravitational path integral that factorizes, reproduces the Page curve for entropy, and includes operators for baby universe states.

  18. Replica Phase Transition with Quantum Gravity Corrections

    hep-th 2026-02 unverdicted novelty 5.0

    The boundary theory of near-extremal RN black holes shows a replica phase transition controlled by temperature and the couplings C, K, and E.

  19. Semi-classical spacetime thermodynamics

    hep-th 2025-09 unverdicted novelty 5.0

    Derives semi-classical gravity from thermodynamics of stretched light cones in 2D dilaton gravity with explicit conformal anomaly backreaction and shows equations of motion follow from dynamical Wald entropy in Brans-...

  20. Gravitational Hilbert spaces: invariant and co-invariant states, inner products, gauge-fixing, and BRST

    hep-th 2025-09 unverdicted novelty 4.0

    Reviews construction of physical inner products in canonical quantum gravity via group averaging and BRST formalism, illustrated in mini-superspace models and connected to path integrals.

  21. Albertian Channel Memory in Black-Hole Evaporation

    hep-th 2026-05 unverdicted novelty 3.0

    An Albert algebra description of the horizon yields a Volterra memory law on the Reissner-Nordstrom evaporation trajectory whose spectral overlap reconstructs the Page curve envelope without restoring standard AMPS te...

Reference graph

Works this paper leans on

63 extracted references · 63 canonical work pages · cited by 19 Pith papers · 37 internal anchors

  1. [1]

    S. W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D14, 2460–2473, 1976

    work page 1976

  2. [2]

    D. N. Page, Information in black hole radiation, Phys. Rev. Lett. 71, 3743–3746, 1993, [arXiv:hep-th/9306083 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  3. [3]

    D. N. Page, Time Dependence of Hawking Radiation Entropy, JCAP 1309, 028, 2013, [arXiv:1301.4995 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  4. [4]

    Entanglement Wedge Reconstruction and the Information Paradox

    G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, 2019, [arXiv:1905.08255 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  5. [5]

    The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole

    A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, 2019, [arXiv:1905.08762 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  6. [6]

    The Page curve of Hawking radiation from semiclassical geometry

    A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, 2019, [arXiv:1908.10996 [hep-th]]

    work page internal anchor Pith review arXiv 2019

  7. [7]

    T. G. Mertens, Towards Black Hole Evaporation in Jackiw-Teitelboim Gravity, JHEP 07, 097, 2019, [arXiv:1903.10485 [hep-th]]. 47

    work page arXiv 2019

  8. [8]

    Akers, A

    C. Akers, A. Levine and S. Leichenauer, Large Breakdowns of Entanglement Wedge Reconstruction, 2019, [arXiv:1908.03975 [hep-th]]

    work page arXiv 2019

  9. [9]

    Moitra, S

    U. Moitra, S. K. Sake, S. P. Trivedi and V. Vishal, Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit, 2019, [arXiv:1908.08523 [hep-th]]

    work page arXiv 2019

  10. [10]

    Almheiri, R

    A. Almheiri, R. Mahajan and J. E. Santos, Entanglement islands in higher dimensions, 2019, [arXiv:1911.09666 [hep-th]]

    work page arXiv 2019

  11. [11]

    Fu and D

    Z. Fu and D. Marolf, Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT, JHEP 11, 040, 2019, [arXiv:1909.02505 [hep-th]]

    work page arXiv 2019

  12. [12]

    Zhang, Evaporation dynamics of the Sachdev-Ye-Kitaev model, 2019, [arXiv:1909.10637 [cond-mat.str-el]]

    P. Zhang, Evaporation dynamics of the Sachdev-Ye-Kitaev model, 2019, [arXiv:1909.10637 [cond-mat.str-el]]

    work page arXiv 2019

  13. [13]

    Akers, N

    C. Akers, N. Engelhardt and D. Harlow, Simple holographic models of black hole evaporation, 2019, [arXiv:1910.00972 [hep-th]]

    work page arXiv 2019

  14. [14]

    Almheiri, R

    A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon, 2019, [arXiv:1910.11077 [hep-th]]

    work page arXiv 2019

  15. [15]

    Rozali, J

    M. Rozali, J. Sully, M. Van Raamsdonk, C. Waddell and D. Wakeham, Information radiation in BCFT models of black holes, 2019, [arXiv:1910.12836 [hep-th]]

    work page arXiv 2019

  16. [16]

    H. Z. Chen, Z. Fisher, J. Hernandez, R. C. Myers and S.-M. Ruan, Information Flow in Black Hole Evaporation, 2019, [arXiv:1911.03402 [hep-th]]

    work page arXiv 2019

  17. [17]

    Bousso and M

    R. Bousso and M. Tomasevic, Unitarity From a Smooth Horizon?, 2019, [arXiv:1911.06305 [hep-th]]

    work page arXiv 2019

  18. [18]

    D. L. Jafferis and D. K. Kolchmeyer, Entanglement Entropy in Jackiw-Teitelboim Gravity, 2019, [arXiv:1911.10663 [hep-th]]

    work page arXiv 2019

  19. [19]

    Blommaert, T

    A. Blommaert, T. G. Mertens and H. Verschelde, Eigenbranes in Jackiw-Teitelboim gravity, 2019, [arXiv:1911.11603 [hep-th]]

    work page arXiv 2019

  20. [20]

    Holographic Derivation of Entanglement Entropy from AdS/CFT

    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96, 181602, 2006, [arXiv:hep-th/0603001 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  21. [21]

    V. E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07, 062, 2007, [arXiv:0705.0016 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  22. [22]

    Quantum corrections to holographic entanglement entropy

    T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11, 074, 2013, [arXiv:1307.2892 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  23. [23]

    Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime

    N. Engelhardt and A. C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01, 073, 2015, [arXiv:1408.3203 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  24. [24]

    S. D. Mathur, What is the dual of two entangled CFTs?, 2014, [arXiv:1402.6378 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  25. [25]

    Jackiw, Lower Dimensional Gravity, Nucl

    R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B252, 343–356, 1985. 48

    work page 1985

  26. [26]

    Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys

    C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B126, 41–45, 1983

    work page 1983

  27. [27]

    Models of AdS_2 Backreaction and Holography

    A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11, 014, 2015, [arXiv:1402.6334 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  28. [28]

    Generalized gravitational entropy

    A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08, 090, 2013, [arXiv:1304.4926 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  29. [29]

    X. Dong, A. Lewkowycz and M. Rangamani, Deriving covariant holographic entanglement, JHEP 11, 028, 2016, [arXiv:1607.07506 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  30. [30]

    Entropy, Extremality, Euclidean Variations, and the Equations of Motion

    X. Dong and A. Lewkowycz, Entropy, Extremality, Euclidean Variations, and the Equations of Motion, JHEP 01, 081, 2018, [arXiv:1705.08453 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  31. [31]

    Replica wormholes and the black hole interior

    G. Penington, S. H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, 2019, [arXiv:1911.11977 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  32. [32]

    J. M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04, 021, 2003, [arXiv:hep-th/0106112 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  33. [33]

    P. Saad, S. H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, 2018, [arXiv:1806.06840 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  34. [34]

    P. Saad, S. H. Shenker and D. Stanford, JT gravity as a matrix integral, 2019, [arXiv:1903.11115 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  35. [35]

    Saad, Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity, 2019, [arXiv:1910.10311 [hep-th]]

    P. Saad, Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity, 2019, [arXiv:1910.10311 [hep-th]]

    work page arXiv 2019

  36. [36]

    J. V. Rocha, Evaporation of large black holes in AdS: Coupling to the evaporon, JHEP 08, 075, 2008, [arXiv:0804.0055 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  37. [37]

    An Investigation of AdS$_2$ Backreaction and Holography

    J. Engelsoy, T. G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07, 139, 2016, [arXiv:1606.03438 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  38. [38]

    An Alternative to Compactification

    L. Randall and R. Sundrum, An Alternative to compactification, Phys. Rev. Lett. 83, 4690–4693, 1999, [arXiv:hep-th/9906064 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  39. [39]

    Locally Localized Gravity

    A. Karch and L. Randall, Locally localized gravity, JHEP 05, 008, 2001, [arXiv:hep-th/0011156 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  40. [40]

    Maldacena, A

    J. Maldacena, A. Milekhin and F. Popov, Traversable wormholes in four dimensions, 2018, [arXiv:1807.04726 [hep-th]]

    work page arXiv 2018

  41. [41]

    T. M. Fiola, J. Preskill, A. Strominger and S. P. Trivedi, Black hole thermodynamics and information loss in two-dimensions, Phys. Rev. D50, 3987–4014, 1994, [arXiv:hep-th/9403137 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  42. [42]

    C. G. Callan, Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B333, 55–61, 1994, [arXiv:hep-th/9401072 [hep-th]]. 49

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  43. [43]

    Entanglement entropy in free quantum field theory

    H. Casini and M. Huerta, Entanglement entropy in free quantum field theory, J. Phys. A42, 504007, 2009, [arXiv:0905.2562 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  44. [44]

    Holographic Entanglement Entropy for General Higher Derivative Gravity

    X. Dong, Holographic Entanglement Entropy for General Higher Derivative Gravity, JHEP 01, 044, 2014, [arXiv:1310.5713 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  45. [45]

    Sharon and D

    E. Sharon and D. Mumford, 2D-Shape Analysis Using Conformal Mapping, International Journal of Computer Vision 70, 55, 2006

    work page 2006

  46. [46]

    Chaos in AdS$_2$ holography

    K. Jensen, Chaos and hydrodynamics near AdS 2, 2016, [arXiv:1605.06098 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  47. [47]

    Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space

    J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016, 12C104, 2016, [arXiv:1606.01857 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  48. [48]

    Entanglement Entropy and Quantum Field Theory

    P. Calabrese and J. L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406, P06002, 2004, [arXiv:hep-th/0405152 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  49. [49]

    Entanglement and alpha entropies for a massive Dirac field in two dimensions

    H. Casini, C. D. Fosco and M. Huerta, Entanglement and alpha entropies for a massive Dirac field in two dimensions, J. Stat. Mech. 0507, P07007, 2005, [arXiv:cond-mat/0505563 [cond-mat]]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  50. [50]

    Learning the Alpha-bits of Black Holes,

    P. Hayden and G. Penington, Learning the Alpha-bits of Black Holes, 2018, [arXiv:1807.06041 [hep-th]]

    work page arXiv 2018

  51. [51]

    Hayden and G

    P. Hayden and G. Penington, Approximate quantum error correction revisited: Introducing the alpha-bit, 2017

    work page 2017

  52. [52]

    D. L. Jafferis, A. Lewkowycz, J. Maldacena and S. J. Suh, Relative entropy equals bulk relative entropy, JHEP 06, 004, 2016, [arXiv:1512.06431 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  53. [53]

    X. Dong, D. Harlow and A. C. Wall, Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality, Phys. Rev. Lett. 117, 021601, 2016, [arXiv:1601.05416 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  54. [54]

    Bulk Locality and Quantum Error Correction in AdS/CFT

    A. Almheiri, X. Dong and D. Harlow, Bulk Locality and Quantum Error Correction in AdS/CFT, JHEP 04, 163, 2015, [arXiv:1411.7041 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  55. [55]

    Microscopic Origin of the Bekenstein-Hawking Entropy

    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B379, 99–104, 1996, [arXiv:hep-th/9601029 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  56. [56]

    S. W. Hawking, Quantum Coherence Down the Wormhole, Phys. Lett. B195, 337, 1987

    work page 1987

  57. [57]

    G. V. Lavrelashvili, V. A. Rubakov and P. G. Tinyakov, Disruption of Quantum Coherence upon a Change in Spatial Topology in Quantum Gravity, JETP Lett. 46, 167–169, 1987

    work page 1987

  58. [58]

    S. B. Giddings and A. Strominger, Axion Induced Topology Change in Quantum Gravity and String Theory, Nucl. Phys. B306, 890–907, 1988

    work page 1988

  59. [59]

    S. R. Coleman, Black Holes as Red Herrings: Topological Fluctuations and the Loss of Quantum Coherence, Nucl. Phys. B307, 867–882, 1988. 50

    work page 1988

  60. [60]

    S. B. Giddings and A. Strominger, Loss of Incoherence and Determination of Coupling Constants in Quantum Gravity, Nucl. Phys. B307, 854–866, 1988

    work page 1988

  61. [61]

    A Possible Resolution of the Black Hole Information Puzzle

    J. Polchinski and A. Strominger, A Possible resolution of the black hole information puzzle, Phys. Rev. D50, 7403–7409, 1994, [arXiv:hep-th/9407008 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  62. [62]

    Time Evolution of Entanglement Entropy from Black Hole Interiors

    T. Hartman and J. Maldacena, Time Evolution of Entanglement Entropy from Black Hole Interiors, JHEP 05, 014, 2013, [arXiv:1303.1080 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  63. [63]

    Entanglement is not Enough

    L. Susskind, Entanglement is not enough, Fortsch. Phys. 64, 49–71, 2016, [arXiv:1411.0690 [hep-th]]. 51

    work page internal anchor Pith review Pith/arXiv arXiv 2016