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arxiv: 2606.23776 · v1 · pith:NOX3QF3Gnew · submitted 2026-06-22 · ✦ hep-th

On the amplitude expansion of gluon correlators in textrm{AdS}₄

Humberto Gomez , Renann Lipinski Jusinskas , Arthur Lipstein , Cristhiam Lopez-Arcos This is my paper

Pith reviewed 2026-06-26 07:07 UTC · model grok-4.3

classification ✦ hep-th
keywords gluon correlatorsAdS4flat-space amplitudesBerends-Giele currentsenergy polestree-levelholographycurvature corrections
1
0 comments X

The pith

Tree-level gluon correlators in AdS4 decompose into sums over energy poles whose residues are flat-space amplitudes at all multiplicities.

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

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.

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

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.

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.

Where Pith is reading between the lines

These are 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.

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.

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.

read the original 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.

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 / 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

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.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 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 no independent evidence
    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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Forward citations

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