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On the amplitude expansion of gluon correlators in $\textrm{AdS}_4$

T0 review · 2 major / 0 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read Tree-level gluon correlators in AdS4 decompose into sums over energy poles whose residues are flat-space amplitudes at all multiplicities.

desk verdict The paper gives a recursive construction for all-multiplicity AdS4 gluon correlators from flat-space amplitudes via AdS Berends-Giele currents, but only checks it explicitly to five points. read the letter →

arxiv 2606.23776 v1 pith:NOX3QF3G submitted 2026-06-22 hep-th

Humberto Gomez , Renann Lipinski Jusinskas , Arthur Lipstein , Cristhiam Lopez-Arcos This is my paper · ORCID
classification hep-th
keywords gluoncorrelatorsAdS4flat-spaceamplitudesBerends-Gielecurrentsenergypolestree-levelholographycurvaturecorrections
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper establishes that tree-level gluon correlators in four-dimensional anti-de Sitter space admit an expansion in terms of flat-space scattering amplitudes for arbitrary numbers of points. Each n-point correlator splits into a sum of terms featuring energy poles, with the residues at those poles given exactly by the corresponding flat-space amplitudes. Curvature corrections from the AdS geometry enter through lower-point amplitudes in which some external polarizations have been merged. These mergers are defined recursively by an AdS version of Berends-Giele currents. The resulting formulas reproduce explicit Feynman-diagram results up to five points and operate on the full correlator rather than diagram by diagram.

What carries the argument

The AdS analogue of the Berends-Giele currents, which recursively merge external polarizations to produce the curvature corrections at each multiplicity.

What would settle it

An explicit six-point gluon correlator computed both by direct Feynman diagrams and by the recursive pole expansion, if the two results disagree, would falsify the claim.

Watch

Extended reading notes

Core claim

Tree-level gluon correlators in AdS4 admit a natural expansion in terms of flat-space scattering amplitudes at all multiplicities. In particular, every n-point correlator can be decomposed into a sum over energy poles whose residues are flat-space amplitudes. The n-point amplitude encodes the flat-space limit while curvature corrections are captured by lower-point amplitudes with merged external data. The merging of external polarizations is recursively defined via an AdS analogue of the Berends-Giele currents, giving rise to all-multiplicity formulae which we verify against Feynman diagram computations up to five points. Crucially, the approach works at the level of full correlators rather

Load-bearing premise

The recursive AdS analogue of the Berends-Giele currents correctly captures every curvature correction and reproduces the full correlator for arbitrary n.

Editorial extensions

If this is right

  • The leading term in each energy-pole residue is precisely the flat-space n-point amplitude.
  • All curvature corrections at n points are expressed using amplitudes with fewer external legs whose data have been merged.
  • Repeated application of the recursion produces explicit closed-form expressions for correlators of any multiplicity.
  • The decomposition applies directly to the complete correlator, bypassing the need to sum individual diagrams.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same pole structure may apply to other fields or to higher-dimensional AdS spaces once an appropriate recursive current is identified.
  • Holographic computations could become simpler by importing known flat-space amplitudes and only evaluating the merged lower-point corrections.
  • A mismatch at six or higher points would indicate that additional non-recursive curvature terms are required.
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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

2 major / 0 minor

Summary. The paper claims that tree-level gluon correlators in AdS₄ admit a natural expansion in flat-space scattering amplitudes at all multiplicities. Every n-point correlator decomposes into a sum over energy poles whose residues are flat-space amplitudes; the n-point term encodes the flat-space limit while curvature corrections arise from lower-point amplitudes with merged external data. The merging is defined recursively via an AdS analogue of the Berends-Giele currents, yielding explicit all-multiplicity formulae that are verified against Feynman diagrams up to five points. The method is presented as operating at the level of full correlators rather than individual diagrams.

Significance. If the recursive construction is shown to hold generally, the result would be significant as it supplies an elegant recursive construction that reduces AdS correlator computation to known flat-space amplitudes plus a merging procedure, providing a transparent alternative to direct diagrammatic calculations in curved space. Credit is due for the full-correlator perspective and the explicit all-multiplicity formulae, even though their generality is currently supported only by limited verification.

major comments (2)
  1. [Abstract] Abstract: the central all-multiplicity claim rests on the assertion that the AdS Berends-Giele recursion captures every curvature correction for arbitrary n, yet the manuscript states that the resulting formulae are verified against Feynman diagrams only up to five points, with no inductive argument, structural proof, or statement of the precise matching criterion provided to establish that the recursion exhausts all AdS corrections beyond n=5.
  2. [Abstract] Abstract: the verification is described only as 'against Feynman diagram computations up to five points' without error bars, a precise matching criterion, or confirmation that the check covers the full correlator (rather than selected components), which is load-bearing for assessing whether the recursion reproduces the complete AdS result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed report and constructive feedback on our manuscript. We address the two major comments point by point below, agreeing where the presentation requires clarification and outlining the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central all-multiplicity claim rests on the assertion that the AdS Berends-Giele recursion captures every curvature correction for arbitrary n, yet the manuscript states that the resulting formulae are verified against Feynman diagrams only up to five points, with no inductive argument, structural proof, or statement of the precise matching criterion provided to establish that the recursion exhausts all AdS corrections beyond n=5.

    Authors: The AdS Berends-Giele recursion is constructed precisely so that each step merges lower-point data to account for all curvature corrections at the given multiplicity; the all-multiplicity formulae follow directly from iterating this procedure. The recursive definition itself supplies the structural argument that every correction is captured, without requiring an additional inductive step. We acknowledge, however, that the manuscript does not spell out this reasoning explicitly or provide a formal statement of the matching criterion. We will revise the abstract and the relevant sections to clarify that the formulae are obtained by recursive application of the AdS currents, which by construction exhausts the curvature corrections at every n, and to state the precise sense in which the five-point checks validate the implementation. revision: partial

  2. Referee: [Abstract] Abstract: the verification is described only as 'against Feynman diagram computations up to five points' without error bars, a precise matching criterion, or confirmation that the check covers the full correlator (rather than selected components), which is load-bearing for assessing whether the recursion reproduces the complete AdS result.

    Authors: We agree that the current description of the verification is insufficiently detailed. The checks were performed on the full correlators by comparing the complete set of energy-pole residues and the curvature corrections obtained from the recursion against independent Feynman-diagram results, with exact symbolic agreement required. In the revised manuscript we will expand this description, specify the matching criterion (coefficient-by-coefficient equality in the energy-pole expansion), confirm that the entire correlator was compared at each multiplicity, and note that the computations are exact (hence no error bars). revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: recursion and flat-space inputs are independent; verification is explicit up to n=5

full rationale

The derivation defines an AdS analogue of Berends-Giele currents as a new recursive merging rule for external data, takes known flat-space amplitudes as external inputs, and checks the resulting pole-residue formulae against Feynman diagrams only up to five points. No equation reduces a claimed prediction to a fitted parameter or to a self-referential definition; no load-bearing step rests on a self-citation chain. The all-multiplicity statement is an unproven extrapolation rather than a circular reduction, so the construction remains self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 0 assumptions · 1 invented entities

Abstract-only review supplies no explicit free parameters, background axioms, or invented entities beyond the stated recursive current; the central construction therefore rests on the unstated assumption that the AdS current recursion is well-defined and complete.

invented entities (1)
  • AdS analogue of Berends-Giele currents
    purpose: Recursive definition of merged external polarizations that encode curvature corrections
    Introduced in the abstract as the mechanism that generates all curvature corrections from lower-point data.

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Cite this review

Pith. "Pith review of On the amplitude expansion of gluon correlators in $\textrm{AdS}_4$." pith.science (2026). https://pith.science/paper/NOX3QF3G

@misc{pith2026260623776,
  author       = {Pith},
  title        = {Pith review of: On the amplitude expansion of gluon correlators in $\textrmAdS_4$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NOX3QF3G}},
  note         = {Machine review of arXiv:2606.23776}
}
abstract

We show that tree-level gluon correlators in $\textrm{AdS}_4$ admit a natural expansion in terms of flat-space scattering amplitudes at all multiplicities. In particular, every $n$-point correlator can be decomposed into a sum over energy poles whose residues are flat-space amplitudes. The $n$-point amplitude encodes the flat-space limit while curvature corrections are captured by lower-point amplitudes with merged external data. The merging of external polarizations is recursively defined via an AdS analogue of the Berends-Giele currents, giving rise to all-multiplicity formulae which we verify against Feynman diagram computations up to five points. Crucially, our approach works at the level of full correlators rather than individual diagrams, providing an elegant and transparent alternative to conventional approaches for computing correlators in anti-de Sitter space.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    Perturbiner multi-particle solutions of classical field equations generate Berends–Giele currents and tree-level amplitudes across scalars, gauge theory, gravity, NLSM, AdS, and one-loop integrands, including several ...

  2. Dirichlet, Neumann, Mixed and self-dual holography: (self-dual) Yang--Mills theory II

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    Derives bulk and boundary propagators and computes 3- and 4-point correlators for YM, CS and SDYM in AdS/CFT with multiple boundary conditions to relate their observables.

Reference graph

Works this paper leans on

42 extracted references · 36 canonical work pages · cited by 2 Pith papers

  1. [1]

    On the amplitude expansion of gluon correlators in $\textrm{AdS}_4$

    in terms of merged external data. Together, these two observations allow us to establish all-multiplicity formulae for gluon correlators in AdS4 in terms of flat- space amplitude data alone. An important feature of our approach is that it operates at the level of full correlators, rather than individual Feynman diagrams. The amplitude expansion structure ...

    work page Pith review arXiv 2026

  2. [2]

    J. M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP05, 013, arXiv:astro-ph/0210603

    work page Pith review arXiv

  3. [3]

    Implications of conformal invariance in momentum space

    A. Bzowski, P. McFadden, and K. Skenderis, Implications 7 of conformal invariance in momentum space, JHEP03, 111, arXiv:1304.7760 [hep-th]

    work page Pith review arXiv

  4. [4]

    New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators

    S. Raju, New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators, Phys. Rev. D85, 126009 (2012), arXiv:1201.6449 [hep-th]

    work page Pith review arXiv 2012

  5. [5]

    F.A.BerendsandW.T.Giele,RecursiveCalculationsfor Processes with n Gluons, Nucl. Phys. B306, 759 (1988)

    1988

  6. [6]

    Snowmass White Paper: The Cosmological Bootstrap

    D. Baumann, D. Green, A. Joyce, E. Pajer, G. L. Pimentel, C. Sleight, and M. Taronna, Snowmass White Paper: The Cosmological Bootstrap, SciPost Phys. Comm. Rep.2024, 1 (2024), arXiv:2203.08121 [hep-th]

    work page Pith review arXiv 2024

  7. [7]

    The interpretation in terms of energy is more transparent in de Sitter space, where the bulk direction is timelike and the boundary is Euclidean

  8. [8]

    L. J. Dixon, Calculating scattering amplitudes efficiently, inTheoretical Advanced Study Institute in Elementary Particle Physics (TASI 95): QCD and Beyond(1996) pp. 539–584, arXiv:hep-ph/9601359

    work page Pith review arXiv 1996

Show all 42 references
  1. [9]

    Arkani-Hamed, P

    N. Arkani-Hamed, P. Benincasa, and A. Postnikov, Cosmological Polytopes and the Wavefunction of the Universe, arXiv preprint (2017), arXiv:1709.02813 [hep- th]

    2017 arXiv

  2. [10]

    Albayrak, C

    S. Albayrak, C. Chowdhury, and S. Kharel, Study of momentum space scalar amplitudes in AdS spacetime, Phys. Rev. D101, 124043 (2020), arXiv:2001.06777 [hep- th]

    2020

  3. [11]

    Baumann, C

    D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee, and G. L. Pimentel, The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization, SciPost Phys.11, 071 (2021), arXiv:2005.04234 [hep-th]

    2021

  4. [12]

    Arkani-Hamed, D

    N. Arkani-Hamed, D. Baumann, H. Lee, and G. L. Pimentel, The Cosmological Bootstrap: Inflationary CorrelatorsfromSymmetriesandSingularities,JHEP04, 105, arXiv:1811.00024 [hep-th]

  5. [13]

    Goodhew, S

    H. Goodhew, S. Jazayeri, and E. Pajer, The Cosmological Optical Theorem, JCAP04, 021, arXiv:2009.02898 [hep- th]

    2009

  6. [14]

    Jazayeri, E

    S. Jazayeri, E. Pajer, and D. Stefanyszyn, From locality and unitarity to cosmological correlators, JHEP10, 065, arXiv:2103.08649 [hep-th]

  7. [15]

    Melville and E

    S. Melville and E. Pajer, Cosmological Cutting Rules, JHEP05, 249, arXiv:2103.09832 [hep-th]

    arXiv

  8. [16]

    A Mathematica notebook with these comparisons is attached to the arXiv submission

  9. [17]

    Liu and A

    H. Liu and A. A. Tseytlin, On four point functions in the CFT / AdS correspondence, Phys. Rev. D59, 086002 (1999), arXiv:hep-th/9807097

    1999 arXiv

  10. [18]

    Raju, Recursion Relations for AdS/CFT Correlators, Phys

    S. Raju, Recursion Relations for AdS/CFT Correlators, Phys. Rev. D83, 126002 (2011), arXiv:1102.4724 [hep- th]

    2011 arXiv

  11. [19]

    J. M. Maldacena and G. L. Pimentel, On graviton non-Gaussianities during inflation, JHEP09, 045, arXiv:1104.2846 [hep-th]

    arXiv

  12. [20]

    Albayrak and S

    S. Albayrak and S. Kharel, Towards the higher point holographic momentum space amplitudes, JHEP02, 040, arXiv:1810.12459 [hep-th]

    arXiv

  13. [21]

    In AdS this corresponds to a non-covariant gauge- choice

    Note that we are referring to Lorenz gauge in half of flat space. In AdS this corresponds to a non-covariant gauge- choice

  14. [22]

    Armstrong, A

    C. Armstrong, A. E. Lipstein, and J. Mei, Color/kinematics duality in AdS 4, JHEP02, 194, arXiv:2012.02059 [hep-th]

    2012

  15. [23]

    Albayrak, C

    S. Albayrak, C. Chowdhury, and S. Kharel, New relation for Witten diagrams, JHEP10, 274, arXiv:1904.10043 [hep-th]

    1904

  16. [24]

    S. J. Parke and T. R. Taylor, An Amplitude fornGluon Scattering, Phys. Rev. Lett.56, 2459 (1986)

    1986

  17. [25]

    Hodges, Eliminating spurious poles from gauge- theoretic amplitudes, JHEP05, 135, arXiv:0905.1473 [hep-th]

    A. Hodges, Eliminating spurious poles from gauge- theoretic amplitudes, JHEP05, 135, arXiv:0905.1473 [hep-th]

    arXiv

  18. [26]

    Adamo, M

    T. Adamo, M. Bullimore, L. Mason, and D. Skinner, Scattering Amplitudes and Wilson Loops in Twistor Space, J. Phys. A44, 454008 (2011), arXiv:1104.2890 [hep-th]

    2011 arXiv

  19. [27]

    Bittleston, G

    R. Bittleston, G. Bogna, S. Heuveline, A. Kmec, L. Mason, and D. Skinner, On AdS 4 deformations of celestial symmetries, JHEP07, 010, arXiv:2403.18011 [hep-th]

  20. [28]

    Baumann, G

    D. Baumann, G. Mathys, G. L. Pimentel, and F. Rost, A new twist on spinning (A)dS correlators, JHEP01, 202, arXiv:2408.02727 [hep-th]

  21. [29]

    Arundine, D

    M. Arundine, D. Baumann, M. H. G. Lee, G. L. Pimentel, and F. Rost, The Cosmological Grassmannian, arXiv (2026), arXiv:2602.07117 [hep-th]

    2026 arXiv

  22. [30]

    Albayrak, S

    S. Albayrak, S. Kharel, and D. Meltzer, On duality of color and kinematics in (A)dS momentum space, JHEP 03, 249, arXiv:2012.10460 [hep-th]

    2012

  23. [31]

    Armstrong, H

    C. Armstrong, H. Goodhew, A. Lipstein, and J. Mei, Graviton trispectrum from gluons, JHEP08, 206, arXiv:2304.07206 [hep-th]

  24. [32]

    Lipstein and S

    A. Lipstein and S. Nagy, Self-Dual Gravity and Color- Kinematics Duality in AdS4, Phys. Rev. Lett.131, 081501 (2023), arXiv:2304.07141 [hep-th]

    2023

  25. [33]

    Chowdhury, G

    C. Chowdhury, G. Doran, A. Lipstein, R. Monteiro, S. Nagy, and K. Singh, Light-cone actions and correlators of self-dual theories in AdS4, JHEP01, 172, arXiv:2411.04172 [hep-th]

  26. [34]

    Gomez, R

    H. Gomez, R. Lipinski Jusinskas, A. Lipstein, and C. Lopez-Arcos, to appear, arXiv (2026)

    2026

  27. [35]

    Arkani-Hamed, Y

    N. Arkani-Hamed, Y. Bai, S. He, and G. Yan, Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet, JHEP05, 096, arXiv:1711.09102 [hep-th]

    arXiv

  28. [36]

    Gomez, R

    H. Gomez, R. L. Jusinskas, and A. Lipstein, Cosmological Scattering Equations, Phys. Rev. Lett.127, 251604 (2021), arXiv:2106.11903 [hep-th]

    2021

  29. [37]

    Arkani-Hamed, C

    N. Arkani-Hamed, C. Figueiredo, and F. Vazão, Cosmohedra, JHEP11, 029, arXiv:2412.19881 [hep-th]

  30. [38]

    A. A. Rosly and K. G. Selivanov, On amplitudes in selfdual sector of Yang-Mills theory, Phys. Lett.B399, 135 (1997), arXiv:hep-th/9611101 [hep-th]

    1997 arXiv

  31. [39]

    A. A. Rosly and K. G. Selivanov, Gravitational SD perturbiner, arXiv (1997), arXiv:hep-th/9710196 [hep- th]

    1997 arXiv

  32. [40]

    C. R. Mafra and O. Schlotterer, Solution to the nonlinear field equations of ten dimensional supersymmetric Yang-Mills theory, Phys. Rev.D92, 066001 (2015), arXiv:1501.05562 [hep-th]

    2015 arXiv

  33. [41]

    Armstrong, H

    C. Armstrong, H. Gomez, R. Lipinski Jusinskas, A. Lipstein, and J. Mei, New recursion relations for tree- level correlators in anti–de Sitter spacetime, Phys. Rev. D106, L121701 (2022), arXiv:2209.02709 [hep-th]

    2022

  34. [42]

    Skvortsov and R

    E. Skvortsov and R. Van Dongen, Dirichlet, Neumann, Mixed and self-dual holography: (self-dual) Yang-Mills theory, arXiv (2026), arXiv:2602.21658 [hep-th]

    2026

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