Pith. sign in

REVIEW 3 major objections 5 minor 67 references

This paper claims that the exponent d(g) governing the large-spin OPE coefficient of two maximal giant gravitons and a twist-two operator is free of finite-size corrections and can be computed exactly at any coupling.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 07:19 UTC pith:IRGEFEQ7

load-bearing objection A promising and novel candidate for a finite-coupling OPE-coefficient observable, but the "exact at any coupling" claim rests on an unproven all-order vanishing that is only checked to low orders. the 3 major comments →

arxiv 2607.21472 v1 pith:IRGEFEQ7 submitted 2026-07-23 hep-th

A universal scaling function for giant graviton OPE coefficients

Miao He , Yunfeng Jiang This is my paper
classification hep-th
keywords giant gravitonsOPE coefficientslarge spin limitscaling functionN=4 super-Yang-MillsintegrabilityBES equationAdS/CFT
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper studies the three-point function of two maximal giant gravitons and a twist-two operator in planar N=4 super-Yang-Mills theory. It claims that in the large-spin limit the OPE coefficient D_S(g) scales as 2^{-S+1/2} S^{d(g)}, and that the exponent d(g) is independent of the finite twist of the spinning operator. Because of this, the asymptotic Bethe-ansatz expression, valid before finite-size effects, determines d(g) exactly at any 't Hooft coupling. The authors develop a systematic procedure to compute d(g): the weak-coupling series matches available field-theory results through three loops, the strong-coupling series gives new predictions, and a numerical evaluation at finite coupling interpolates smoothly between the two regimes. A sympathetic reader would care because this would be the first OPE-coefficient quantity computable across the full coupling range, offering a counterpart to the cusp anomalous dimension.

Core claim

The central claim is that the scaling exponent d(g) in D_S(g) ~ 2^{-S+1/2} S^{d(g)} receives no finite-size corrections. This means the all-order asymptotic expression for the OPE coefficient, derived from the worldsheet g-function formalism, can be used to determine d(g) exactly. In the large-spin limit, the ratio of Gaudin-like determinants contributes only -1/4 log S at leading order, with all higher-loop corrections vanishing (they begin at order 1/S); the entire coupling dependence of d(g) comes from the prefactor, which is an integral involving the boundary dressing phase and the BES density fluctuation. The paper presents weak-coupling results through seven loops (with matching to thr

What carries the argument

The central object is the scaling function d(g), extracted from the log S coefficient of the large-spin OPE coefficient. The argument runs through the asymptotic Bethe ansatz: the Bethe-root density is the universal BES density, independent of twist, and the ratio of Gaudin-like determinants reduces to a series of multiple integrals over the scattering kernel alone, giving -1/4 log S with no higher-loop log corrections. The prefactor, involving the boundary dressing phase and the density fluctuation, supplies the coupling-dependent part. The key identity is that in the large-spin limit the diagonal Gaudin weight M_j equals 2πρ(u_j), so that density information cancels in the determinant rati

Load-bearing premise

The entire argument rests on the identification that, for the ground state at finite twist, the large-spin Bethe-root density is exactly the BES density with no hole contribution; this has only been verified numerically up to three loops at finite spin, and if holes or twist-dependent corrections survive at higher loops the exponent d(g) would shift.

What would settle it

Compute the OPE coefficient D_S(g) at four loops in weakly coupled planar N=4 SYM (or via an independent method such as the quantum spectral curve) for a finite twist L and large spin S; if the extracted d(g) deviates from the paper's four-loop prediction, the finite-size-free conjecture fails. Alternatively, a strong-coupling string computation of the two-giant-graviton/twist-two three-point function could check the leading 1/g behavior of eq. (24).

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If correct, the exponent d(g) can be computed exactly from asymptotic data, without finite-size TBA, at any value of the 't Hooft coupling.
  • The weak-coupling expansion of d(g) provides a testable prediction beyond three loops; the four-loop term is the first new prediction.
  • The strong-coupling expansion gives concrete predictions for the emission of a GKP string from a D3-brane, awaiting an independent string-theory computation.
  • The finite-coupling interpolation suggests a smooth crossover between weak and strong coupling, similar to the cusp anomalous dimension.
  • The universality of d(g) across twists L implies that the same exponent governs OPE coefficients with any finite twist for the twist-two operator.

Where Pith is reading between the lines

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

  • Editorial inference: If d(g) is truly finite-size free, the same large-spin limit might yield subleading corrections that are universal functions of the twist — the paper notes these would be twist-dependent — and an all-coupling systematic expansion in 1/S could become accessible with similar integrability tools.
  • Editorial inference: The method may generalize to other three-point functions with integrable boundary states, such as defect one-point functions or Coulomb-branch one-point functions; the paper suggests this, and one could test whether analogous exponents d(g) appear and are finite-size free.
  • Editorial inference: A direct check of the conjecture at four loops in field theory — or via the quantum spectral curve — would either confirm or break the claim that finite-size corrections vanish, since the numerical M_j check is only up to three loops at finite S.
  • Editorial inference: Because d(g) is a pure function of coupling and independent of L, it may be a candidate for a 'universal' quantity that could be matched to a simple string-theory observable, perhaps the energy density of a particular string configuration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies the large-spin limit S→∞ of the OPE coefficient D_S(g) for two maximal giant gravitons and a twist-two operator in planar N=4 SYM. Starting from the asymptotic integrability expression (3), the authors take the large-spin limit and propose that, up to normalization, D_S(g) ∼ 2^{-S+1/2} S^{d(g)} with an exponent d(g) free of finite-size corrections. They argue that the prefactor P(S) is controlled by the BES density and boundary dressing phase, and that the ratio of Gaudin-like determinants R(S) remains exactly -1/4 log S at all loops. This yields weak-coupling expansions (23) (matching independent field-theory results to three loops), strong-coupling predictions (24), and a finite-coupling numerical interpolation in Fig. 2. The central all-loop claim is explicitly acknowledged as a conjecture supported by evidence at low orders.

Significance. If the main conjecture holds, this is a notable advance: it would provide an OPE-coefficient analogue of the cusp anomalous dimension, computable at any coupling from integrability and—unlike most OPE data—free of finite-size corrections. The paper gives concrete, falsifiable predictions: the four-loop coefficient in (23) and the first strong-coupling terms in (24). The three-loop agreement with the independent field-theory bootstrap [45] is a genuine anchor. The authors also provide a transparent numerical implementation for finite coupling. The main weakness is that the exactness of d(g) rests on an unproven all-loop statement about the Gaudin-determinant ratio, verified only through order g^4, together with a numerical check of the density identification up to g^6 at S=200. Thus the significance is high if the conjecture is correct, but the current manuscript does not establish that rigorously.

major comments (3)
  1. [§'All-loop result', Eq. (22); Supp. Eqs. (S13)–(S15)] The exactness of d(g) at all couplings hinges on Eq. (22): lim_{S→∞} R(S) = -1/4 log S, with no higher-loop corrections at log-S order. The only explicit computations shown are R^{(2)} and R^{(4)} in Eqs. (S13)–(S15). The statement that this 'can be systematized at higher loop orders' is not a proof, and no g^6 or higher check is supplied. Since Eqs. (23), (24), and Fig. 2 all use Eq. (22), the all-coupling result is a conjecture, not a derivation. I recommend either providing an all-order argument (e.g., a uniform estimate showing the n-loop contribution is O(1/S)), or explicitly labeling the all-loop result as conjectural and restricting 'exact' to the orders that are actually proven.
  2. [Supp. Eq. (S8) and Fig. S1; main-text Eq. (19)] The replacement M_j → 2πρ(u_j) is an input to the cancellation that produces Eq. (S9) and hence Eq. (22). It assumes that the hole density ρ_hole vanishes for the ground state at finite twist L. The numerical evidence in Fig. S1 is only up to g^6 at S=200. If a hole contribution or an L-dependent correction survives at higher loops, the factor 1/M_j would not cancel against the density in the measure, and R(S) would acquire additional log-S terms. This is not a minor technicality: it is the same load-bearing soft spot as Eq. (22), and it should be either proven or clearly stated as an assumption that limits the certainty of the central claim.
  3. [Abstract and Introduction; Discussion paragraph] The abstract states that 'the all-loop asymptotic expression for the OPE coefficient can be used to determine d(g) exactly', and the Introduction repeats this. The Discussion, by contrast, concedes that the argument is 'strong evidence ... rather than a rigorous proof'. This mismatch is significant because the exactness claim is the paper's main selling point. Please reconcile the wording: either upgrade the evidence to a proof, or state in the abstract/Introduction that the all-loop exactness is a well-motivated conjecture with verified low-order checks. As it stands, the presentation overstates the status of Eq. (22).
minor comments (5)
  1. [Eq. (21)] The first integral in Eq. (21) appears to contain a stray 'du' after the integration measure dt; presumably the measure should be dt only. Please check and correct.
  2. [Fig. 1 and Fig. S1 captions] The captions say 'up to g^6 order' in different notations ('up to g^6', 'at g^6 order'), while the main text refers to 'up to three-loop'. Clarify the convention so that loop order and g-order are not confusing to the reader.
  3. [Eq. (3) and surrounding text] The overbar on D_S(g) in Eq. (3) is introduced in prose only ('the overbar indicates that the result is asymptotic'). Define this notation explicitly at the equation, since it is used in the main derivation.
  4. [References] Reference [45] is cited as an arXiv preprint (arXiv:2605.14281). If the journal requires published references, please update once it is available in a journal, or note its status.
  5. [Eq. (23)] The text says 'the result up to four-loop order reads' but the series is shown to g^8. Make clear that g^8 is indeed four-loop and that the g^4, g^6 terms match [45] while g^8 is a prediction.

Circularity Check

0 steps flagged

No significant circularity: d(g) is extracted from an asymptotic formalism via a new large-spin analysis, and the independent three-loop match anchors the result; the all-order conjecture is a limitation, not a circular step.

full rationale

The paper's central quantity d(g) is not an input to the cited framework. The derivation starts from the asymptotic expression (3) taken from [31,32] (which share an author), but d(g) is obtained by a new large-spin analysis of the prefactor (20)-(21) and the determinant ratio R(S). Equation (22), the claim that higher-loop corrections to R(S) vanish at log-S order, is verified explicitly only through order g^4 in the supplement (S13-S15); the paper itself says this 'can be systematized' and that the absence of finite-size corrections is 'strong evidence ... rather than a rigorous proof' (Universal scaling function section). That is an unproven conjecture/omitted proof, which is a correctness risk, not a circular reduction: Eq. (22) is not defined in terms of d(g), and no fitted parameter is renamed as a prediction. The weak-coupling series (23) agrees with the independent field-theoretic bootstrap [45] through three loops, providing external validation that the asymptotic expression is being used correctly. The four-loop term and the strong-coupling series (24) are genuine predictions, not fits. Self-citations [31,32] supply the starting formalism, but because the target coefficient is new and the three-loop match is external, the reasoning does not reduce to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 0 invented entities

No data-fitting parameters appear; the input is integrability machinery from [11,31,32] plus the finite-size-free conjecture. The central claim rests on unproven assumptions explicitly flagged by the authors.

axioms (6)
  • domain assumption The exact asymptotic worldsheet g-function expression for D_S(g), eq. (3), from [31,32] is correct.
    The paper's starting point; [31,32] are prior works by one of the present authors (Jiang), and no independent reproduction is cited.
  • domain assumption In the large spin limit with finite twist L, the Bethe-root density and mode numbers are those of the BES equation, with vanishing hole density for the ground state (eq. S8).
    Justified only numerically up to three loops for finite S; all-loop validity is assumed.
  • ad hoc to paper The scaling exponent d(g) is free of finite-size corrections.
    Stated explicitly as a conjecture in the Discussions; not proven. It is needed to identify the asymptotic large-S coefficient with the exact d(g).
  • ad hoc to paper Higher-loop corrections to the ratio of Gaudin-like determinants do not contribute to the log S term; R(S) = -1/4 log S at all loops.
    Demonstrated for R^(2) and R^(4) in the supplemental material (eq. S15); claimed to hold at all orders without a general proof.
  • standard math The BES equation [11] and Bessel-matrix numerical solution [12] provide the all-loop density fluctuation.
    Imported from established integrability literature; not rederived here.
  • domain assumption The boundary dressing phase log σ_B(u) computed in [31] is correct at all orders.
    Used in the prefactor, eqs. (20)-(21); self-cited prior derivation.

pith-pipeline@v1.3.0-alltime-deepseek · 15792 in / 13574 out tokens · 126677 ms · 2026-08-01T07:19:36.552391+00:00 · methodology

0 comments
read the original abstract

We consider the large spin limit $S\to\infty$ of the OPE coefficient for two maximal giant gravitons and a spinning operator with finite twist in planar $\mathcal{N}=4$ super-Yang-Mills theory. Up to an overall normalization factor, this OPE coefficient exhibits a power-law scaling of the form $S^{d(g)}$. We provide strong evidence that the exponent $d(g)$ is free from finite size corrections. Consequently, the all-loop asymptotic expression for the OPE coefficient can be used to determine $d(g)$ exactly. We develop a systematic method to compute the scaling function $d(g)$ for arbitrary values of the 't Hooft coupling $g$. At weak coupling, our result agrees perfectly with the available field-theoretic results up to three-loop order. At strong coupling, we present the first three orders as concrete predictions. We further provide the finite-coupling result and show that it interpolates smoothly between the weak- and strong-coupling regimes.

Figures

Figures reproduced from arXiv: 2607.21472 by Miao He, Yunfeng Jiang.

Figure 1
Figure 1. Figure 1: FIG. 1. We plot the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The scaling function is shown. The black dots repre [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

discussion (0)

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

Reference graph

Works this paper leans on

67 extracted references · 61 linked inside Pith

  1. [1]

    Three loop universal anomalous dimension of the Wilson operators inN= 4 SUSY Yang-Mills model,

    A. V. Kotikov, L. N. Lipatov, A. I. Onishchenko, and V. N. Velizhanin, “Three loop universal anomalous dimension of the Wilson operators inN= 4 SUSY Yang-Mills model,”Phys. Lett. B595(2004) 521–529, arXiv:hep-th/0404092. [Erratum: Phys.Lett.B 632, 754–756 (2006)]

    Pith/arXiv arXiv 2004

  2. [2]

    The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory,

    Z. Bern, M. Czakon, L. J. Dixon, D. A. Kosower, and V. A. Smirnov, “The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory,”Phys. Rev. D75 (2007) 085010,arXiv:hep-th/0610248

    Pith/arXiv arXiv 2007

  3. [3]

    The full four-loop cusp anomalous dimension inN= 4 super Yang-Mills and QCD,

    J. M. Henn, G. P. Korchemsky, and B. Mistlberger, “The full four-loop cusp anomalous dimension inN= 4 super Yang-Mills and QCD,”JHEP04(2020) 018, arXiv:1911.10174 [hep-th]

    Pith/arXiv arXiv 2020

  4. [4]

    A Semiclassical limit of the gauge / string correspondence,

    S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “A Semiclassical limit of the gauge / string correspondence,”Nucl. Phys. B636(2002) 99–114, arXiv:hep-th/0204051

    Pith/arXiv arXiv 2002

  5. [5]

    Semiclassical quantization of rotating superstring in AdS(5) x S**5,

    S. Frolov and A. A. Tseytlin, “Semiclassical quantization of rotating superstring in AdS(5) x S**5,” JHEP06(2002) 007,arXiv:hep-th/0204226

    Pith/arXiv arXiv 2002

  6. [6]

    A Note on twist two operators in N=4 SYM and Wilson loops in Minkowski signature,

    M. Kruczenski, “A Note on twist two operators in N=4 SYM and Wilson loops in Minkowski signature,”JHEP 12(2002) 024,arXiv:hep-th/0210115

    Pith/arXiv arXiv 2002

  7. [7]

    Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS(5) x S**5,

    M. Kruczenski, R. Roiban, A. Tirziu, and A. A. Tseytlin, “Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS(5) x S**5,”Nucl. Phys. B791(2008) 93–124, arXiv:0707.4254 [hep-th]

    Pith/arXiv arXiv 2008

  8. [8]

    Two-loop world-sheet corrections in AdS(5) x S**5 superstring,

    R. Roiban, A. Tirziu, and A. A. Tseytlin, “Two-loop world-sheet corrections in AdS(5) x S**5 superstring,” JHEP07(2007) 056,arXiv:0704.3638 [hep-th]

    Pith/arXiv arXiv 2007

  9. [9]

    Integrability and transcendentality,

    B. Eden and M. Staudacher, “Integrability and transcendentality,”J. Stat. Mech.0611(2006) P11014, arXiv:hep-th/0603157

    Pith/arXiv arXiv 2006

  10. [10]

    A Crossing-symmetric phase for AdS(5) x S**5 strings,

    N. Beisert, R. Hernandez, and E. Lopez, “A Crossing-symmetric phase for AdS(5) x S**5 strings,” JHEP11(2006) 070,arXiv:hep-th/0609044

    Pith/arXiv arXiv 2006

  11. [11]

    Transcendentality and Crossing,

    N. Beisert, B. Eden, and M. Staudacher, “Transcendentality and Crossing,”J. Stat. Mech.0701 (2007) P01021,arXiv:hep-th/0610251

    Pith/arXiv arXiv 2007

  12. [12]

    A Test of the AdS/CFT correspondence using high-spin operators,

    M. K. Benna, S. Benvenuti, I. R. Klebanov, and A. Scardicchio, “A Test of the AdS/CFT correspondence using high-spin operators,”Phys. Rev. Lett.98(2007) 131603,arXiv:hep-th/0611135

    Pith/arXiv arXiv 2007

  13. [13]

    Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling,

    B. Basso, G. P. Korchemsky, and J. Kotanski, “Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling,”Phys. Rev. Lett. 100(2008) 091601,arXiv:0708.3933 [hep-th]

    Pith/arXiv arXiv 2008

  14. [14]

    Long-range psu(2,2—4) Bethe Ansatze for gauge theory and strings,

    N. Beisert and M. Staudacher, “Long-range psu(2,2—4) Bethe Ansatze for gauge theory and strings,”Nucl. Phys. B727(2005) 1–62,arXiv:hep-th/0504190

    Pith/arXiv arXiv 2005

  15. [15]

    Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory,

    N. Gromov, V. Kazakov, and P. Vieira, “Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory,”Phys. Rev. Lett. 103(2009) 131601,arXiv:0901.3753 [hep-th]

    Pith/arXiv arXiv 2009

  16. [16]

    Thermodynamic Bethe Ansatz for the AdS(5) x S(5) Mirror Model,

    G. Arutyunov and S. Frolov, “Thermodynamic Bethe Ansatz for the AdS(5) x S(5) Mirror Model,”JHEP05 (2009) 068,arXiv:0903.0141 [hep-th]

    Pith/arXiv arXiv 2009

  17. [17]

    Quantum Spectral Curve for PlanarN= 4 Super-Yang-Mills Theory,

    N. Gromov, V. Kazakov, S. Leurent, and D. Volin, “Quantum Spectral Curve for PlanarN= 4 Super-Yang-Mills Theory,”Phys. Rev. Lett.112no. 1, (2014) 011602,arXiv:1305.1939 [hep-th]

    Pith/arXiv arXiv 2014

  18. [18]

    Tailoring Three-Point Functions and Integrability,

    J. Escobedo, N. Gromov, A. Sever, and P. Vieira, “Tailoring Three-Point Functions and Integrability,” JHEP09(2011) 028,arXiv:1012.2475 [hep-th]

    Pith/arXiv arXiv 2011

  19. [19]

    N=4 SYM structure constants as determinants,

    O. Foda, “N=4 SYM structure constants as determinants,”JHEP03(2012) 096,arXiv:1111.4663 [math-ph]

    Pith/arXiv arXiv 2012

  20. [20]

    Quantum Integrability for Three-Point Functions of Maximally Supersymmetric Yang-Mills Theory,

    N. Gromov and P. Vieira, “Quantum Integrability for Three-Point Functions of Maximally Supersymmetric Yang-Mills Theory,”Phys. Rev. Lett.111no. 21, (2013) 211601,arXiv:1202.4103 [hep-th]

    Pith/arXiv arXiv 2013

  21. [21]

    Fermionic Correlators from Integrability,

    J. Caetano and T. Fleury, “Fermionic Correlators from Integrability,”JHEP09(2016) 010,arXiv:1607.02542 [hep-th]

    Pith/arXiv arXiv 2016

  22. [22]

    Tailoring Non-Compact Spin Chains,

    P. Vieira and T. Wang, “Tailoring Non-Compact Spin Chains,”JHEP10(2014) 035,arXiv:1311.6404 [hep-th]

    Pith/arXiv arXiv 2014

  23. [23]

    Fixing the Quantum Three-Point Function,

    Y. Jiang, I. Kostov, F. Loebbert, and D. Serban, “Fixing the Quantum Three-Point Function,”JHEP04 (2014) 019,arXiv:1401.0384 [hep-th]

    Pith/arXiv arXiv 2014

  24. [24]

    Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory,

    B. Basso, S. Komatsu, and P. Vieira, “Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory,”arXiv:1505.06745 [hep-th]

    Pith/arXiv arXiv

  25. [25]

    Gluing Hexagons at Three Loops,

    B. Basso, V. Goncalves, S. Komatsu, and P. Vieira, “Gluing Hexagons at Three Loops,”Nucl. Phys. B907 (2016) 695–716,arXiv:1510.01683 [hep-th]

    Pith/arXiv arXiv 2016

  26. [26]

    Structure constants at wrapping order,

    B. Basso, V. Goncalves, and S. Komatsu, “Structure constants at wrapping order,”JHEP05(2017) 124, arXiv:1702.02154 [hep-th]

    Pith/arXiv arXiv 2017

  27. [27]

    The hexagon in the mirror: the three-point function in the SoV representation,

    Y. Jiang, S. Komatsu, I. Kostov, and D. Serban, “The hexagon in the mirror: the three-point function in the SoV representation,”J. Phys. A49no. 17, (2016) 174007,arXiv:1506.09088 [hep-th]

    Pith/arXiv arXiv 2016

  28. [28]

    Structure constants in N=4 supersymmetric Yang-Mills theory and separation of variables,

    C. Bercini, A. Homrich, and P. Vieira, “Structure constants in N=4 supersymmetric Yang-Mills theory and separation of variables,”Phys. Rev. D110no. 12, (2024) L121901,arXiv:2210.04923 [hep-th]

    Pith/arXiv arXiv 2024

  29. [29]

    Structure Constants from Q-Systems and Separation of Variables,

    T. Bargheer, C. Bercini, G. Lefundes, and P. Ryan, “Structure Constants from Q-Systems and Separation of Variables,”arXiv:2603.26617 [hep-th]

    arXiv

  30. [30]

    Structure Constants of Short Operators in Planar N=4 Supersymmetric Yang-Mills Theory,

    B. Basso, A. Georgoudis, and A. K. Sueiro, “Structure Constants of Short Operators in Planar N=4 Supersymmetric Yang-Mills Theory,”Phys. Rev. Lett. 130no. 13, (2023) 131603,arXiv:2207.01315 [hep-th]

    Pith/arXiv arXiv 2023

  31. [31]

    Structure constants inN= 4 SYM at finite coupling as worldsheet g-function,

    Y. Jiang, S. Komatsu, and E. Vescovi, “Structure constants inN= 4 SYM at finite coupling as worldsheet g-function,”JHEP07no. 07, (2020) 037, arXiv:1906.07733 [hep-th]. 7

    Pith/arXiv arXiv 2020

  32. [32]

    Exact Three-Point Functions of Determinant Operators in PlanarN= 4 Supersymmetric Yang-Mills Theory,

    Y. Jiang, S. Komatsu, and E. Vescovi, “Exact Three-Point Functions of Determinant Operators in PlanarN= 4 Supersymmetric Yang-Mills Theory,” Phys. Rev. Lett.123no. 19, (2019) 191601, arXiv:1907.11242 [hep-th]

    Pith/arXiv arXiv 2019

  33. [33]

    On correlation functions of operators dual to classical spinning string states,

    R. A. Janik, P. Surowka, and A. Wereszczynski, “On correlation functions of operators dual to classical spinning string states,”JHEP05(2010) 030, arXiv:1002.4613 [hep-th]

    Pith/arXiv arXiv 2010

  34. [34]

    Holographic three-point functions of semiclassical states,

    K. Zarembo, “Holographic three-point functions of semiclassical states,”JHEP09(2010) 030, arXiv:1008.1059 [hep-th]

    Pith/arXiv arXiv 2010

  35. [35]

    On three-point correlation functions in the gauge/gravity duality,

    M. S. Costa, R. Monteiro, J. E. Santos, and D. Zoakos, “On three-point correlation functions in the gauge/gravity duality,”JHEP11(2010) 141, arXiv:1008.1070 [hep-th]

    Pith/arXiv arXiv 2010

  36. [36]

    On semiclassical computation of 3-point functions of closed string vertex operators inAdS 5xS5,

    R. Roiban and A. A. Tseytlin, “On semiclassical computation of 3-point functions of closed string vertex operators inAdS 5xS5,”Phys. Rev. D82(2010) 106011, arXiv:1008.4921 [hep-th]

    Pith/arXiv arXiv 2010

  37. [37]

    HHL correlators, orbit averaging and form factors,

    Z. Bajnok, R. A. Janik, and A. Wereszczy´ nski, “HHL correlators, orbit averaging and form factors,”JHEP09 (2014) 050,arXiv:1404.4556 [hep-th]

    Pith/arXiv arXiv 2014

  38. [38]

    Correlation functions of three heavy operators: The AdS contribution,

    R. A. Janik and A. Wereszczynski, “Correlation functions of three heavy operators: The AdS contribution,”JHEP12(2011) 095,arXiv:1109.6262 [hep-th]

    Pith/arXiv arXiv 2011

  39. [39]

    On holographic three point functions for GKP strings from integrability,

    Y. Kazama and S. Komatsu, “On holographic three point functions for GKP strings from integrability,” JHEP01(2012) 110,arXiv:1110.3949 [hep-th]. [Erratum: JHEP 06, 150 (2012)]

    Pith/arXiv arXiv 2012

  40. [40]

    Wave functions and correlation functions for GKP strings from integrability,

    Y. Kazama and S. Komatsu, “Wave functions and correlation functions for GKP strings from integrability,”JHEP09(2012) 022,arXiv:1205.6060 [hep-th]

    Pith/arXiv arXiv 2012

  41. [41]

    Three-point functions in the SU(2) sector at strong coupling,

    Y. Kazama and S. Komatsu, “Three-point functions in the SU(2) sector at strong coupling,”JHEP03(2014) 052,arXiv:1312.3727 [hep-th]

    Pith/arXiv arXiv 2014

  42. [42]

    Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills,

    N. Drukker and J. Plefka, “Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills,”JHEP04(2009) 052,arXiv:0901.3653 [hep-th]

    Pith/arXiv arXiv 2009

  43. [43]

    All giant graviton two-point functions at two-loops,

    Y. Wu, Y. Jiang, C. Liu, and Y. Zhang, “All giant graviton two-point functions at two-loops,”JHEP03 (2026) 097,arXiv:2509.23161 [hep-th]

    arXiv 2026

  44. [44]

    Giant correlators at quantum level,

    Y. Jiang, Y. Wu, and Y. Zhang, “Giant correlators at quantum level,”JHEP05(2024) 345, arXiv:2311.16791 [hep-th]

    Pith/arXiv arXiv 2024

  45. [45]

    Bootstrapping Giant Graviton Correlators,

    S. He, C. Shi, Y. Tang, and C. Wen, “Bootstrapping Giant Graviton Correlators,”arXiv:2605.14281 [hep-th]

    Pith/arXiv arXiv

  46. [46]

    D-branes and orbit average,

    P. Yang, Y. Jiang, S. Komatsu, and J.-B. Wu, “D-branes and orbit average,”SciPost Phys.12no. 2, (2022) 055,arXiv:2103.16580 [hep-th]

    Pith/arXiv arXiv 2022

  47. [47]

    Giant Graviton Correlators as Defect Systems,

    J. Chen, Y. Jiang, and X. Zhou, “Giant Graviton Correlators as Defect Systems,”Phys. Rev. Lett.135 no. 8, (2025) 081602,arXiv:2503.22987 [hep-th]

    Pith/arXiv arXiv 2025

  48. [48]

    Defect approach to giant graviton dynamics,

    J. Chen, Y. Jiang, and X. Zhou, “Defect approach to giant graviton dynamics,”Rept. Prog. Phys.89no. 6, (2026) 067801,arXiv:2602.13570 [hep-th]

    arXiv 2026

  49. [49]

    Exact results for giant graviton four-point correlators,

    A. Brown, F. Galvagno, and C. Wen, “Exact results for giant graviton four-point correlators,”JHEP07(2024) 049,arXiv:2403.17263 [hep-th]

    Pith/arXiv arXiv 2024

  50. [50]

    Universality of giant graviton correlators,

    A. Brown, D. Dorigoni, F. Galvagno, and C. Wen, “Universality of giant graviton correlators,”JHEP11 (2025) 034,arXiv:2508.15657 [hep-th]

    arXiv 2025

  51. [51]

    Absorption of closed strings by giant gravitons,

    G. Chen, R. de Mello Koch, M. Kim, and H. J. R. Van Zyl, “Absorption of closed strings by giant gravitons,”JHEP10(2019) 133,arXiv:1908.03553 [hep-th]

    Pith/arXiv arXiv 2019

  52. [52]

    Higher-spin correlators,

    L. F. Alday and A. Bissi, “Higher-spin correlators,” JHEP10(2013) 202,arXiv:1305.4604 [hep-th]

    Pith/arXiv arXiv 2013

  53. [53]

    One-point Functions in Defect CFT and Integrability,

    M. de Leeuw, C. Kristjansen, and K. Zarembo, “One-point Functions in Defect CFT and Integrability,” JHEP08(2015) 098,arXiv:1506.06958 [hep-th]

    Pith/arXiv arXiv 2015

  54. [54]

    One-loop one-point functions in gauge-gravity dualities with defects,

    I. Buhl-Mortensen, M. de Leeuw, A. C. Ipsen, C. Kristjansen, and M. Wilhelm, “One-loop one-point functions in gauge-gravity dualities with defects,”Phys. Rev. Lett.117no. 23, (2016) 231603, arXiv:1606.01886 [hep-th]

    Pith/arXiv arXiv 2016

  55. [55]

    Asymptotic One-Point Functions in Gauge-String Duality with Defects,

    I. Buhl-Mortensen, M. de Leeuw, A. C. Ipsen, C. Kristjansen, and M. Wilhelm, “Asymptotic One-Point Functions in Gauge-String Duality with Defects,”Phys. Rev. Lett.119no. 26, (2017) 261604, arXiv:1704.07386 [hep-th]

    Pith/arXiv arXiv 2017

  56. [56]

    Non-perturbative defect one-point functions in planarN= 4 super-Yang-Mills,

    S. Komatsu and Y. Wang, “Non-perturbative defect one-point functions in planarN= 4 super-Yang-Mills,” Nucl. Phys. B958(2020) 115120,arXiv:2004.09514 [hep-th]

    Pith/arXiv arXiv 2020

  57. [57]

    ’t Hooft loops and integrability,

    C. Kristjansen and K. Zarembo, “’t Hooft loops and integrability,”JHEP08(2023) 184,arXiv:2305.03649 [hep-th]

    Pith/arXiv arXiv 2023

  58. [58]

    ’t Hooft loops in N=4 super-Yang-Mills,

    C. Kristjansen and K. Zarembo, “’t Hooft loops in N=4 super-Yang-Mills,”JHEP02(2025) 179, arXiv:2412.01972 [hep-th]

    Pith/arXiv arXiv 2025

  59. [59]

    Vacuum Condensates on the Coulomb Branch,

    V. Ivanovskiy, S. Komatsu, V. Mishnyakov, N. Terziev, N. Zaigraev, and K. Zarembo, “Vacuum Condensates on the Coulomb Branch,”arXiv:2405.19043 [hep-th]

    Pith/arXiv arXiv

  60. [60]

    Coulomb branch and integrability,

    F. Coronado, S. Komatsu, and K. Zarembo, “Coulomb branch and integrability,”JHEP10(2025) 143, arXiv:2506.07222 [hep-th]

    arXiv 2025

  61. [61]

    Three-point functions in ABJM and Bethe Ansatz,

    P. Yang, Y. Jiang, S. Komatsu, and J.-B. Wu, “Three-point functions in ABJM and Bethe Ansatz,” JHEP01(2022) 002,arXiv:2103.15840 [hep-th]

    Pith/arXiv arXiv 2022

  62. [62]

    Integrable boundary states from maximal giant gravitons in ABJM theory,

    P. Yang, “Integrable boundary states from maximal giant gravitons in ABJM theory,”Phys. Lett. B846 (2023) 138194,arXiv:2208.12010 [hep-th]

    Pith/arXiv arXiv 2023

  63. [63]

    Structure constants of heavy operators in ABJM and ABJ theory,

    G. Chen, R. De Mello Koch, M. Kim, and H. J. R. Van Zyl, “Structure constants of heavy operators in ABJM and ABJ theory,”Phys. Rev. D100no. 8, (2019) 086019,arXiv:1909.03215 [hep-th]

    Pith/arXiv arXiv 2019

  64. [64]

    Wilson-loop one-point functions in ABJM theory,

    Y. Jiang, J.-B. Wu, and P. Yang, “Wilson-loop one-point functions in ABJM theory,”JHEP09(2023) 047,arXiv:2306.05773 [hep-th]

    Pith/arXiv arXiv 2023

  65. [65]

    Holographic Wilson loop one-point functions in ABJM theory,

    X.-Y. Zhang, Y. Jiang, and J.-B. Wu, “Holographic Wilson loop one-point functions in ABJM theory,” JHEP11(2025) 008,arXiv:2508.00281 [hep-th]

    arXiv 2025

  66. [66]

    Integrable domain walls in ABJM theory,

    C. Kristjansen, D.-L. Vu, and K. Zarembo, “Integrable domain walls in ABJM theory,”JHEP02(2022) 070, arXiv:2112.10438 [hep-th]

    Pith/arXiv arXiv 2022

  67. [67]

    String integrability of the ABJM defect,

    G. Linardopoulos, “String integrability of the ABJM defect,”JHEP06(2022) 033,arXiv:2202.06824 [hep-th]. 8 Supplemental Material for “A universal scaling function for giant graviton OPE coefficient” RA TIO OF GAUDIN-LIKE DETERMINANTS The all-loop Gaudin-like matrices are (G±)jk =M jδjk −(K g(uj, uk)± Kg(uj,−u k)),(S1) where the scattering kernel is given b...

    Pith/arXiv arXiv 2022