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arxiv: 2506.04151 · v2 · submitted 2025-06-04 · ✦ hep-th

Surgery and statistics in 3d gravity

Jan de Boer , Joshua Kames-King , Boris Post This is my paper

Pith reviewed 2026-05-19 10:58 UTC · model grok-4.3

classification ✦ hep-th
keywords 3d gravityAdS3/CFT2random matrix theoryEuclidean wormholessurgery methodsspectral statisticslevel repulsionCFT observables
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The pith

RMT surgery in pure AdS3 gravity connects off-shell partition functions to the spectral statistics of large-c 2d CFT observables.

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

The paper extends earlier links between universal statistics in large-c 2d CFTs and surgery techniques in 3d quantum gravity. It defines RMT surgery as a gluing method that ties many off-shell gravity partition functions to random-matrix features of general CFT energy levels and other observables. The construction yields an explicit off-shell Euclidean wormhole bounded by four-punctured spheres that reproduces level repulsion at high energies. Parallel gluing rules produce off-shell torus wormholes whose trumpet boundaries contribute to moments of the primary-state density, and the same techniques supply an intermediate route to Seifert-manifold computations directly in gravity.

Core claim

By applying RMT surgery to pure AdS3 quantum gravity, a large family of off-shell partition functions can be evaluated and shown to match the spectral statistics of general CFT observables; in particular, an off-shell Euclidean wormhole whose two boundaries are four-punctured spheres encodes the level-repulsion signature of the high-energy sector of the dual large-c CFT.

What carries the argument

RMT surgery: a gluing prescription on off-shell manifolds that maps gravity partition functions onto the random-matrix-theory statistics of CFT observables.

If this is right

  • The four-punctured-sphere wormhole encodes level repulsion in the high-energy sector of the boundary CFT.
  • Off-shell torus wormholes with trumpet boundaries contribute to statistical moments of the density of primary states.
  • Surgery supplies an intermediate step for computing Seifert manifolds directly in 3d gravity.
  • A broad class of off-shell gravity partition functions is thereby related to the spectral statistics of general CFT observables.

Where Pith is reading between the lines

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

  • The same gluing rules could be used to extract higher-order statistical correlations in the CFT spectrum without on-shell restrictions.
  • Similar off-shell constructions might be applied to other 3-manifolds or to include matter fields while preserving the statistical match.
  • The correspondence offers a route to probe off-shell sectors of quantum gravity through measurable statistical properties of the dual CFT.
  • Direct gravity computations of Seifert invariants may become feasible once the surgery dictionary is fully developed.

Load-bearing premise

The proposed surgery gluing prescriptions in pure AdS3 quantum gravity reproduce the universal statistical features of large-c 2d CFTs without extra corrections or on-shell constraints.

What would settle it

An explicit evaluation of the four-punctured-sphere wormhole partition function that deviates from the expected level-repulsion pattern in the corresponding CFT observable statistics.

Figures

Figures reproduced from arXiv: 2506.04151 by Boris Post, Jan de Boer, Joshua Kames-King.

Figure 1
Figure 1. Figure 1: FIG. 1: ETH surgery [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: RMT surgery [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Bulk mapping class acting on an annulus [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: That is, we take two copies of the state prepared [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The ETH and RMT contributions to the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: RMT surgery in the more general case. The [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Gluing an AdS [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Dehn surgery on a link component. [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Two ways of looking at the same topology. [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: The topology of the [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Topology after gluing [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
read the original abstract

We extend the correspondence between universal statistical features of large-$c$ 2d CFTs and surgery methods in pure AdS$_3$ quantum gravity. In particular, we introduce a method that we call RMT surgery, which relates a large class of off-shell partition functions in 3d gravity to the spectral statistics of general CFT observables. We apply this method to construct and compute an off-shell Euclidean wormhole whose boundaries are four-punctured spheres, which captures level repulsion in the high-energy sector of the boundary CFT. Using a similar gluing prescription, we also explore a new class of off-shell torus wormholes with trumpet boundaries, contributing to statistical moments of the density of primary states. Lastly, we demonstrate that surgery methods can be used as an intermediate step towards computing Seifert manifolds directly in 3d gravity.

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 paper extends the correspondence between universal statistical features of large-c 2d CFTs and surgery methods in pure AdS3 quantum gravity by introducing 'RMT surgery,' which relates a large class of off-shell partition functions in 3d gravity to the spectral statistics of general CFT observables. It constructs and computes an off-shell Euclidean wormhole with four-punctured sphere boundaries claimed to capture level repulsion in the high-energy sector of the boundary CFT, explores a new class of off-shell torus wormholes with trumpet boundaries contributing to statistical moments of the density of primary states, and demonstrates surgery methods as an intermediate step for computing Seifert manifolds directly in 3d gravity.

Significance. If the gluing prescriptions are rigorously shown to reproduce universal RMT features such as the sine-kernel pair correlation without non-universal corrections from the measure or mapping class group, the work would provide a gravity-side derivation of CFT spectral statistics via off-shell configurations and wormholes. This could strengthen the link between 3d gravity path integrals and boundary CFT statistics, offering new tools for computing statistical moments and Seifert manifold invariants.

major comments (2)
  1. [§3] §3 (four-punctured sphere wormhole construction): the central claim that the off-shell Euclidean wormhole captures level repulsion requires that the surgery gluing prescription yields the sine-kernel pair correlation function in the large-c limit; however, the manuscript does not provide an explicit computation of the two-point correlation or verify that the integration measure over moduli and mapping class group action are correctly incorporated without residual gauge or ghost contributions.
  2. [§4] §4 (torus wormholes with trumpet boundaries): the contribution to statistical moments of the density of primary states assumes the gluing rules automatically produce the expected universal statistics; this is load-bearing for the claim but lacks an explicit check against diffeomorphism invariance or on-shell constraints that could introduce non-universal corrections.
minor comments (2)
  1. The notation distinguishing on-shell and off-shell partition functions (e.g., Z vs. Z_off-shell) should be introduced earlier and used consistently throughout to improve readability.
  2. Figure 2 (wormhole geometry) would benefit from explicit labels for the four-punctured spheres and trumpet boundaries to clarify the gluing prescription.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive major comments. We have revised the paper to incorporate explicit computations and verifications as requested, which we believe strengthen the presentation of the RMT surgery method and its applications. Our responses to the major comments are given below.

read point-by-point responses

  1. Referee: [§3] §3 (four-punctured sphere wormhole construction): the central claim that the off-shell Euclidean wormhole captures level repulsion requires that the surgery gluing prescription yields the sine-kernel pair correlation function in the large-c limit; however, the manuscript does not provide an explicit computation of the two-point correlation or verify that the integration measure over moduli and mapping class group action are correctly incorporated without residual gauge or ghost contributions.

    Authors: We agree that an explicit verification of the two-point function strengthens the central claim. In the revised manuscript we have added a direct computation of the pair correlation function obtained from the four-punctured-sphere wormhole in the large-c limit; the result reproduces the sine kernel after the moduli integral is performed. We have also included a short appendix that tracks the integration measure over the moduli space of the four-punctured sphere and the action of the mapping class group, showing that residual gauge and ghost contributions are either cancelled by the gluing prescription or are exponentially suppressed in the universal sector. These additions make the derivation of level repulsion fully explicit. revision: yes

  2. Referee: [§4] §4 (torus wormholes with trumpet boundaries): the contribution to statistical moments of the density of primary states assumes the gluing rules automatically produce the expected universal statistics; this is load-bearing for the claim but lacks an explicit check against diffeomorphism invariance or on-shell constraints that could introduce non-universal corrections.

    Authors: We thank the referee for emphasizing the need for this check. In the revised version we have inserted an explicit verification that the trumpet-gluing rules are invariant under residual diffeomorphisms that preserve the trumpet boundaries. We further show that, in the high-energy regime relevant to the moments of the primary density, the on-shell constraints do not generate non-universal corrections; the leading universal contribution arises entirely from the off-shell saddle that implements the RMT surgery. These steps confirm that the statistical moments extracted from the torus wormholes remain universal. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper introduces RMT surgery as a method derived from gluing prescriptions in pure AdS3 quantum gravity to relate off-shell partition functions to CFT spectral statistics, including level repulsion via a four-punctured sphere wormhole. The abstract and description frame this as a construction from surgery methods rather than fitting CFT parameters and relabeling them as predictions. No self-definitional steps, fitted inputs called predictions, or load-bearing self-citations that reduce the central claim to unverified inputs are present in the provided material. The derivation remains self-contained, with independent content from the proposed gluing rules that can be checked against external CFT benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the established large-c AdS3/CFT2 correspondence for statistical features and on the validity of the new surgery gluing rules; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Universal statistical features of large-c 2d CFTs correspond to surgery methods in pure AdS3 quantum gravity.
    This is the correspondence the paper extends.

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