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arxiv: 1911.11977 · v2 · pith:GKAYC3OKnew · submitted 2019-11-27 · ✦ hep-th · gr-qc· quant-ph

Replica wormholes and the black hole interior

Geoff Penington , Stephen H. Shenker , Douglas Stanford , Zhenbin Yang This is my paper

Pith reviewed 2026-05-18 18:43 UTC · model grok-4.3

classification ✦ hep-th gr-qcquant-ph
keywords replica wormholesPage curveblack hole evaporationentanglement entropyholographyJT gravitySYK modelPetz map
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0 comments X

The pith

Replica wormholes connecting different copies justify the holographic Page curve for black hole evaporation.

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

The paper shows that holographic calculations of the Page curve rely on the replica trick applied to the gravitational path integral. This requires summing over geometries that include spacetime wormholes linking the different replica systems. In a simple model the transition from linear growth to saturation in the radiation entropy arises when wormhole topologies dominate. The mechanism is checked in JT gravity with conformal matter and in the SYK model. A wormhole contribution also supplies a direct gravitational derivation of the Petz map for reconstructing the black hole interior from the radiation.

Core claim

Summing replica wormhole geometries in the gravitational path integral implements the replica trick for entanglement entropy. In a simple model, geometries with different numbers of wormholes produce the Page transition in the entropy of Hawking radiation. The same wormhole saddles appear in JT gravity coupled to matter and in the SYK model. The approach also yields an explicit gravitational formula for the Petz map that reconstructs the entanglement wedge of the black hole interior.

What carries the argument

Replica wormhole geometries in the gravitational path integral, which connect multiple replicas and whose inclusion and summation over topologies generates the correct Page curve for black hole radiation entropy.

If this is right

  • The entropy of the Hawking radiation follows the Page curve at late times.
  • The black hole interior is reconstructible from the radiation via the Petz map.
  • The gravity description implicitly averages over an ensemble of boundary theories.
  • Replica wormhole effects control entanglement calculations in both JT gravity and the SYK model.

Where Pith is reading between the lines

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

  • The ensemble interpretation may link to questions about which boundary theory is dual to a given bulk geometry.
  • The same wormhole technique could be applied to other information-theoretic quantities in holographic models.
  • Replica wormholes might supply a general tool for computing late-time entanglement in systems with nontrivial topology.

Load-bearing premise

The gravitational path integral receives important non-perturbative contributions from replica wormhole geometries with connected topologies.

What would settle it

An explicit evaluation of the replica partition function that uses only disconnected geometries and fails to produce the Page transition in the simple model.

read the original abstract

Recent work has shown how to obtain the Page curve of an evaporating black hole from holographic computations of entanglement entropy. We show how these computations can be justified using the replica trick, from geometries with a spacetime wormhole connecting the different replicas. In a simple model, we study the Page transition in detail by summing replica geometries with different topologies. We compute related quantities in less detail in more complicated models, including JT gravity coupled to conformal matter and the SYK model. Separately, we give a direct gravitational argument for entanglement wedge reconstruction using an explicit formula known as the Petz map; again, a spacetime wormhole plays an important role. We discuss an interpretation of the wormhole geometries as part of some ensemble average implicit in the gravity description.

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 recent holographic computations of the Page curve for evaporating black holes can be justified using the replica trick applied to gravitational path integrals that include spacetime wormhole geometries connecting different replicas. In a simple model the authors sum over replica topologies with different connectivities to reproduce the Page transition explicitly. They sketch related calculations in JT gravity coupled to conformal matter and in the SYK model, give a direct gravitational derivation of entanglement-wedge reconstruction via the Petz map (again invoking a wormhole saddle), and discuss an ensemble-average interpretation of the wormhole contributions.

Significance. If the central claims hold, the work supplies a gravitational mechanism that derives the island formula and the Page curve from the replica trick, thereby addressing a key aspect of the black-hole information paradox within semiclassical gravity. The explicit topology summation performed in the simple model constitutes a concrete, falsifiable check of the proposed mechanism and is a clear strength of the manuscript.

major comments (2)
  1. [Section 3] Section 3: the replacement of the usual disconnected replica geometries by connected wormhole saddles is introduced as a postulate within an incompletely specified gravitational path integral; no UV completion or explicit measure is supplied that would justify why these non-perturbative saddles dominate and produce the Page transition. This assumption is load-bearing for the claimed justification of the island formula.
  2. [Discussion section] The ensemble-average interpretation of the wormhole geometries is presented as a plausible reading rather than a derived result; if this interpretation is intended to be part of the central claim, a more precise statement of what is derived versus conjectured is required.
minor comments (2)
  1. The notation for the replica index n and the on-shell actions of the various saddles could be standardized across sections to improve readability for readers outside the immediate subfield.
  2. A brief comparison table or figure summarizing the Page-transition behavior across the simple model, JT, and SYK would help readers assess the generality of the replica-wormhole mechanism.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their thoughtful review and for highlighting the strengths of our manuscript, including the explicit topology summation in the simple model. We address the major comments below and have revised the manuscript accordingly to improve clarity on the assumptions and interpretations.

read point-by-point responses

  1. Referee: [Section 3] Section 3: the replacement of the usual disconnected replica geometries by connected wormhole saddles is introduced as a postulate within an incompletely specified gravitational path integral; no UV completion or explicit measure is supplied that would justify why these non-perturbative saddles dominate and produce the Page transition. This assumption is load-bearing for the claimed justification of the island formula.

    Authors: We agree that the inclusion of connected wormhole saddles is a key assumption in our analysis of Section 3. The gravitational path integral is treated in a semiclassical approximation where we identify the relevant saddles, motivated by the replica trick and the need to reproduce the Page curve. While we do not provide a full UV completion, which remains an open question in quantum gravity, we explicitly demonstrate in the simple model how summing over replica topologies with wormholes leads to the Page transition. We have added text in the revised manuscript to more clearly state the assumptions underlying the path integral and to emphasize that our results are within the semiclassical regime. This should help clarify the justification for the island formula. revision: partial

  2. Referee: [Discussion section] The ensemble-average interpretation of the wormhole geometries is presented as a plausible reading rather than a derived result; if this interpretation is intended to be part of the central claim, a more precise statement of what is derived versus conjectured is required.

    Authors: We appreciate this point. The ensemble-average interpretation is indeed discussed as a possible way to understand the wormhole contributions in the context of the gravity description, but it is not central to our main claims about the replica trick justification and the Petz map. We have revised the discussion section to explicitly distinguish between the derived results from our calculations and the conjectural interpretation regarding ensemble averages. This includes a clearer statement that the main results hold independently of adopting this interpretation. revision: yes

standing simulated objections not resolved
  • A complete UV completion or explicit measure for the gravitational path integral that rigorously justifies the dominance of the non-perturbative wormhole saddles.

Circularity Check

0 steps flagged

No significant circularity; replica wormholes introduced as new saddles

full rationale

The paper applies the standard replica trick to gravitational path integrals and proposes connected wormhole geometries as additional non-perturbative saddles whose on-shell actions produce the Page transition. This step is not self-definitional, does not rename a fitted input as a prediction, and does not rest on a load-bearing self-citation whose content reduces to the present claim. The replica trick and holographic dictionary are invoked from prior literature as external tools, while the wormhole topologies are added as an independent assumption within the gravitational sum. No equation equates a derived quantity to an input parameter by construction, and the central result (island formula via replica wormholes) retains independent content beyond any cited works. The derivation is therefore self-contained against the paper's own stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard holographic dictionary and the replica trick; the new element is the inclusion of connected wormhole saddles whose contribution is not derived from a more microscopic theory but is motivated by the need to reproduce the Page curve.

axioms (1)
  • domain assumption The gravitational path integral includes non-perturbative contributions from replica wormhole geometries.
    Invoked when the authors sum over topologies in the simple model to obtain the Page transition.

pith-pipeline@v0.9.0 · 5657 in / 1289 out tokens · 36041 ms · 2026-05-18T18:43:34.322916+00:00 · methodology

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