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arxiv: 2605.14281 · v2 · pith:46RGY5KKnew · submitted 2026-05-14 · ✦ hep-th

Bootstrapping Giant Graviton Correlators

Song He , Canxin Shi , Yichao Tang , Congkao Wen This is my paper

Pith reviewed 2026-05-19 16:58 UTC · model grok-4.3

classification ✦ hep-th
keywords giant gravitonsfour-point correlatorsbootstrap methodsN=4 super Yang-Millsloop integrandshidden symmetryOPE limitssupersymmetric localization
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The pith

Bootstrap methods fix mixed correlators with giant gravitons through three loops in 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 develops bootstrap methods for four-point correlators mixing giant graviton operators of dimension order N with a light chiral primary operator in N=4 super-Yang-Mills theory at large N. It expands the loop integrand in a basis of labelled f-graphs that include non-planar topologies required by the heavy operators and determines the coefficients from double-triangle and triangle rules in cusp and OPE limits, results from supersymmetric localization, and a ten-dimensional hidden symmetry. These inputs together fix the correlator uniquely through three loops. For the maximal determinant operator the method recovers all known results through two loops and supplies the complete three-loop correction. A reader cares because the approach gives access to perturbative data for heavy operators that resist standard planar techniques.

Core claim

The combination of double-triangle and triangle rules derived from cusp and OPE limits, integrated correlators obtained from supersymmetric localization, and the ten-dimensional hidden symmetry uniquely determines the mixed heavy-light four-point correlator through three loops; for the maximal determinant operator the construction reproduces all previously known results through two loops and yields the full three-loop correction.

What carries the argument

The expansion of the loop integrand in a basis of labelled f-graphs whose coefficients are fixed by bootstrap conditions from cusp and OPE limits, localization, and ten-dimensional hidden symmetry.

If this is right

  • The same inputs fix correlators involving generic chiral primaries via the hidden symmetry.
  • The determined correlator satisfies additional non-trivial consistency checks at three loops.
  • Known two-loop results for the maximal determinant operator are recovered exactly.
  • The three-loop correction for the maximal determinant operator is obtained for the first time.

Where Pith is reading between the lines

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

  • The bootstrap could extend to higher loop orders or to other heavy operators if the underlying rules continue to hold.
  • The method may provide cross-checks with holographic calculations of giant-graviton correlators in the dual string theory.
  • Similar hidden-symmetry and limit-based constraints might apply to mixed correlators in other conformal theories with integrable structures.

Load-bearing premise

The ten-dimensional hidden symmetry and the double-triangle and triangle rules derived from cusp and OPE limits remain valid for correlators containing dimension-N giant graviton operators.

What would settle it

An independent three-loop computation of the maximal-determinant correlator by direct Feynman diagrams or holographic methods that disagrees with the bootstrapped result.

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 / 2 minor

Summary. The manuscript develops bootstrap methods for mixed heavy-light four-point correlators ⟨GGOO⟩ in 𝒩=4 super-Yang-Mills at large N, where G denotes giant graviton operators of dimension ∼N (including the maximal determinant) and O is the chiral primary in the stress-tensor multiplet. The loop integrand is expanded in a basis of labelled f-graphs that necessarily includes non-planar topologies; coefficients through three loops are fixed by double-triangle and triangle rules extracted from cusp and OPE limits, integrated correlators obtained via supersymmetric localization, and a ten-dimensional hidden symmetry that also permits extension to generic 𝒪_k. The resulting system is claimed to be closed, reproducing all known two-loop data for the maximal-determinant case and yielding the three-loop correction.

Significance. If the bootstrap closure holds, the work provides the first three-loop results for correlators involving dimension-N operators, extending light-operator bootstrap techniques to a regime relevant for giant-graviton dynamics in AdS/CFT. The explicit reproduction of two-loop benchmarks and the parameter-free character of the 10D symmetry input are strengths that would make the three-loop prediction a useful benchmark for future holographic or integrability-based calculations.

major comments (2)
  1. [Bootstrap conditions and 10D symmetry section] The central uniqueness claim rests on the double-triangle and triangle rules remaining unmodified when applied to dimension-N giant gravitons. The manuscript invokes these rules (derived from cusp/OPE limits for light operators) to close the linear system in the labelled f-graph basis, yet does not supply an explicit check that 1/N corrections to OPE coefficients or cusp anomalous dimensions do not generate additional contributions at three-loop order. This assumption is load-bearing; without it the system may become under-determined.
  2. [Results for maximal determinant operator] For the maximal-determinant operator the paper states that known two-loop results are reproduced and the three-loop correction is obtained. The explicit list of all non-vanishing coefficients in the f-graph basis (planar and non-planar) at three loops should be tabulated, together with the rank of the constraint matrix, so that readers can verify that the number of independent conditions equals the number of undetermined coefficients.
minor comments (2)
  1. [Integrand basis] The notation for labelled f-graphs could be illustrated with one concrete non-planar example at two loops to clarify how the labelling encodes the giant-graviton insertions.
  2. [Discussion] A short paragraph comparing the size of the three-loop correction to the two-loop term for the maximal-determinant case would help assess the convergence of the perturbative series.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major comment below, indicating the revisions made where appropriate.

read point-by-point responses

  1. Referee: [Bootstrap conditions and 10D symmetry section] The central uniqueness claim rests on the double-triangle and triangle rules remaining unmodified when applied to dimension-N giant gravitons. The manuscript invokes these rules (derived from cusp/OPE limits for light operators) to close the linear system in the labelled f-graph basis, yet does not supply an explicit check that 1/N corrections to OPE coefficients or cusp anomalous dimensions do not generate additional contributions at three-loop order. This assumption is load-bearing; without it the system may become under-determined.

    Authors: We thank the referee for highlighting this point. The bootstrap is performed strictly at leading order in the large-N limit. In this regime the cusp and OPE limits that define the double-triangle and triangle rules receive no corrections from 1/N effects at three-loop order, as any such corrections to OPE coefficients or anomalous dimensions are suppressed by additional powers of 1/N and enter only at higher orders in the expansion. The 10D hidden symmetry supplies an independent constraint that does not rely on these limits. We have added a short clarifying paragraph in the bootstrap-conditions section to make this reasoning explicit. revision: partial

  2. Referee: [Results for maximal determinant operator] For the maximal-determinant operator the paper states that known two-loop results are reproduced and the three-loop correction is obtained. The explicit list of all non-vanishing coefficients in the f-graph basis (planar and non-planar) at three loops should be tabulated, together with the rank of the constraint matrix, so that readers can verify that the number of independent conditions equals the number of undetermined coefficients.

    Authors: We agree that tabulating the coefficients and reporting the rank of the constraint matrix will allow readers to verify closure directly. In the revised manuscript we have added a new appendix table that lists every non-vanishing coefficient (planar and non-planar) in the labelled f-graph basis at three loops for the maximal-determinant operator, together with the dimension of the basis, the rank of the constraint matrix, and the number of independent conditions. This confirms that the system is fully determined. revision: yes

Circularity Check

0 steps flagged

No significant circularity; bootstrap inputs remain independent

full rationale

The derivation expands the integrand in a labelled f-graph basis and fixes coefficients via independent constraints: double-triangle/triangle rules obtained from cusp and OPE limits, integrated correlators from supersymmetric localization, and ten-dimensional hidden symmetry. These are applied to close the linear system for the mixed heavy-light correlator. The paper reproduces known two-loop results for the maximal determinant operator as an external consistency check before obtaining the three-loop term, rather than fitting parameters to the target data. No equation or self-citation reduces the three-loop output to the inputs by construction, and the central claim is self-contained against external benchmarks such as prior known results and further non-trivial checks.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The central claim rests on standard large-N N=4 SYM assumptions plus the applicability of the listed bootstrap rules to heavy operators; no new free parameters or invented entities are introduced in the abstract.

axioms (3)
  • domain assumption N=4 super-Yang-Mills theory at large N with the standard operator spectrum and OPE structure
    Invoked throughout as the underlying theory whose correlators are being bootstrapped.
  • domain assumption Validity of double-triangle and triangle rules extracted from cusp and OPE limits for dimension-N operators
    Used to fix coefficients; location implied in the bootstrap conditions paragraph of the abstract.
  • domain assumption Ten-dimensional hidden symmetry extends to mixed GGOO correlators with generic chiral primaries O_k
    Cited as allowing extension beyond the stress-tensor multiplet and helping close the system.

pith-pipeline@v0.9.0 · 5723 in / 1753 out tokens · 42527 ms · 2026-05-19T16:58:04.355839+00:00 · methodology

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Reference graph

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