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arxiv: 2605.14281 · v1 · submitted 2026-05-14 · ✦ hep-th

Recognition: 2 theorem links

· Lean Theorem

Bootstrapping Giant Graviton Correlators

Song He , Canxin Shi , Yichao Tang , Congkao Wen
Authors on Pith no claims yet

Pith reviewed 2026-05-15 02:42 UTC · model grok-4.3

classification ✦ hep-th
keywords giant gravitonsbootstrapfour-point correlatorsN=4 super Yang-Millsthree-loop integrandsten-dimensional symmetrysupersymmetric localizationOPE limits
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The pith

Bootstrap conditions from hidden symmetry and cusp limits fix mixed giant-graviton correlators through three loops in large-N N=4 SYM.

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

The paper constructs a systematic bootstrap for four-point functions mixing two giant-graviton operators G of dimension order N with two light chiral primaries O from the stress-tensor multiplet. The loop integrand is written in a basis of labelled f-graphs that includes non-planar topologies required by the heavy operators. Coefficients in this basis are fixed by a combination of integrated correlators obtained from supersymmetric localization, double-triangle and triangle rules extracted from cusp and OPE limits, and a ten-dimensional hidden symmetry that also extends the results to correlators with generic O_k. These inputs together determine the full integrand uniquely through three loops. For the maximal-determinant giant graviton the method reproduces all known two-loop data and supplies the previously unknown three-loop correction.

Core claim

The ten-dimensional hidden symmetry together with the double-triangle and triangle rules in the cusp and OPE limits, supplemented by integrated correlators from supersymmetric localization, fix the coefficients of the labelled f-graph expansion of the integrand for ⟨G G O O⟩ and thereby determine the correlator through three loops. The same data set determines the three-loop correction for the maximal-determinant operator after reproducing all previously known lower-order results.

What carries the argument

A basis of labelled f-graphs (including non-planar topologies) whose coefficients are fixed by ten-dimensional hidden symmetry, cusp/OPE double-triangle rules, and localization-integrated correlators.

If this is right

  • The full three-loop integrand for the maximal-determinant giant-graviton correlator is now known.
  • The same bootstrap data determine correlators involving generic chiral primaries O_k.
  • The method passes additional non-trivial consistency checks beyond the input conditions.
  • The loop integrand remains uniquely fixed even after inclusion of non-planar f-graph topologies required by the heavy operators.

Where Pith is reading between the lines

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

  • If the bootstrap continues to work at four loops it would give the first strong-coupling test of holographic correlators involving two giant gravitons.
  • The same hidden-symmetry and localization inputs might fix mixed correlators with other half-BPS operators of dimension order N.
  • Agreement with a future direct calculation at three loops would confirm that the ten-dimensional symmetry persists without modification in this sector.

Load-bearing premise

The ten-dimensional hidden symmetry and the double-triangle and triangle rules extracted from cusp and OPE limits receive no additional corrections at three loops.

What would settle it

A direct three-loop Feynman-diagram computation for the maximal-determinant operator that produces a result differing from the bootstrapped three-loop correction.

Figures

Figures reproduced from arXiv: 2605.14281 by Canxin Shi, Congkao Wen, Song He, Yichao Tang.

Figure 1
Figure 1. Figure 1: FIG. 1. Labelled [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Three-loop labelled [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
read the original abstract

We develop bootstrap methods for mixed heavy-light four-point correlators $\langle GGOO\rangle$ in $\mathcal N=4$ super-Yang--Mills theory at large $N$, where $O\equiv {\cal O}_2$ is the chiral primary operator in the stress-tensor multiplet and $G$ are (dual) giant graviton operators with dimension of order $N$, including the maximal determinant case. The loop integrand is expanded in a basis of labelled $f$-graphs -- necessarily including non-planar topologies due to the dimension-$N$ nature of the giant gravitons -- and the coefficients are fixed by various bootstrap conditions including double-triangle and triangle rules in the cusp and OPE limits, integrated correlators from supersymmetric localization, and a ten-dimensional hidden symmetry, the latter also allowing extension to correlators involving generic chiral primaries $\mathcal{O}_k$. Together, these inputs uniquely determine the correlator through three loops, passing further non-trivial consistency checks. For the maximal determinant operator, we reproduce the known results through two loops and obtain the full three-loop correction.

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 / 1 minor

Summary. The manuscript develops bootstrap methods for mixed heavy-light four-point correlators ⟨GGOO⟩ in N=4 SYM at large N, with G giant graviton operators of dimension ~N (including the maximal determinant case) and O the stress-tensor multiplet chiral primary. The loop integrand is expanded in a basis of labelled f-graphs that includes non-planar topologies; coefficients are fixed by double-triangle and triangle rules in the cusp and OPE limits, integrated correlators from supersymmetric localization, and a ten-dimensional hidden symmetry that also extends the method to generic O_k. The central claim is that these inputs uniquely determine the correlator through three loops, passing consistency checks, while reproducing known two-loop results for the maximal determinant operator and supplying its three-loop correction.

Significance. If the bootstrap conditions prove complete and unmodified at three loops, the work supplies a concrete advance in computing higher-loop correlators involving heavy operators, furnishing non-planar data and a new three-loop term that can be compared with AdS/CFT expectations. The reproduction of two-loop results and the extension via 10d symmetry are concrete strengths that would be valuable for the literature on giant-graviton correlators.

major comments (2)
  1. [Abstract] Abstract: the statement that the listed inputs 'uniquely determine the correlator through three loops' is load-bearing yet rests on the unverified assumption that the ten-dimensional hidden symmetry and the double-triangle/triangle rules receive no additional corrections or missing structures at three loops for operators of dimension ~N; no explicit test for such deformations is supplied.
  2. [Results section] Results for the maximal determinant operator: the three-loop correction is presented without reported uncertainties, cross-checks against independent localization data, or explicit verification that post-hoc exclusions were not required, which is necessary to substantiate the uniqueness claim given the circularity risk between localization inputs and the target correlator.
minor comments (1)
  1. [Section 2] The notation and labelling convention for the non-planar f-graphs should be illustrated with at least one explicit example to aid readability.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major comment point by point below, proposing revisions where appropriate to strengthen the presentation while preserving the technical content.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that the listed inputs 'uniquely determine the correlator through three loops' is load-bearing yet rests on the unverified assumption that the ten-dimensional hidden symmetry and the double-triangle/triangle rules receive no additional corrections or missing structures at three loops for operators of dimension ~N; no explicit test for such deformations is supplied.

    Authors: We agree that the uniqueness claim would be strengthened by an explicit discussion of the assumptions. The f-graph basis is complete by construction at three loops, the double-triangle and triangle rules follow from the same superconformal Ward identities that hold at lower orders, and the ten-dimensional hidden symmetry is a direct consequence of the PSU(2,2|4) algebra with no known order-dependent deformations. Nevertheless, to address the concern we will revise the abstract to qualify the uniqueness statement as holding under these established conditions and add a short paragraph in the introduction explaining why additional structures are not expected, based on the absence of such deformations in the two-loop case and the rigidity of the labelled f-graph expansion. revision: partial

  2. Referee: [Results section] Results for the maximal determinant operator: the three-loop correction is presented without reported uncertainties, cross-checks against independent localization data, or explicit verification that post-hoc exclusions were not required, which is necessary to substantiate the uniqueness claim given the circularity risk between localization inputs and the target correlator.

    Authors: The three-loop coefficient is fixed by solving the over-determined linear system arising from the full set of bootstrap conditions; the localization integrals enter only as a subset of linear constraints and are independent of the OPE/cusp data. We have explicitly verified that the unique solution satisfies every condition without any post-hoc removal of basis elements. We will add to the results section a statement confirming that no exclusions were required, a brief remark on the numerical precision of the localization integrals, and a note that the inputs are non-circular because the integrated correlator is obtained from a different supersymmetric observable. Independent three-loop localization data for this specific correlator is not available in the literature, so further external cross-checks cannot be performed at present. revision: yes

standing simulated objections not resolved
  • Independent three-loop localization data for the maximal-determinant correlator is not available in the literature, preventing additional external cross-checks beyond the bootstrap consistency tests already performed.

Circularity Check

0 steps flagged

No circularity: bootstrap inputs are independent external constraints

full rationale

The paper expands the loop integrand in a basis of labelled f-graphs and fixes coefficients using double-triangle/triangle rules in cusp/OPE limits, integrated correlators from supersymmetric localization, and ten-dimensional hidden symmetry. It reproduces known two-loop results for the maximal determinant operator before obtaining the three-loop correction, with additional consistency checks. No quoted equation or step reduces a prediction to a fitted input by construction, nor does any load-bearing premise collapse to a self-citation chain or self-definition. The inputs are treated as independent data or symmetry assumptions external to the three-loop target, satisfying the requirement for a self-contained derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The bootstrap relies on supersymmetric localization results, ten-dimensional hidden symmetry, and OPE/cusp limit rules whose independence from the target correlator is not demonstrated in the abstract; no explicit free parameters or new entities are introduced.

axioms (2)
  • domain assumption Ten-dimensional hidden symmetry holds for the correlators
    Invoked to extend results to generic O_k and fix coefficients
  • domain assumption Double-triangle and triangle rules are valid in cusp and OPE limits at three loops
    Used to constrain f-graph coefficients

pith-pipeline@v0.9.0 · 5492 in / 1393 out tokens · 21299 ms · 2026-05-15T02:42:13.322799+00:00 · methodology

discussion (0)

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Reference graph

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