arxiv: 2602.18557 · v2 · submitted 2026-02-20 · ✦ hep-th · math-ph· math.MP

Recognition: 2 theorem links

· Lean Theorem

Strong coupling structure of mathcal{N}=4 SYM observables with matrix Bessel kernel

Bercel Boldis

Authors on Pith no claims yet

Pith reviewed 2026-05-15 20:21 UTC · model grok-4.3

classification ✦ hep-th math-phmath.MP

keywords N=4 SYMstrong couplingtransseriesresurgencematrix Bessel kernelcusp anomalous dimensionoctagon form factor

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The pith

Reorganizing the transseries of matrix Bessel kernel determinants at large 't Hooft coupling reveals a simple relation between each exponentially suppressed correction and the perturbative series for N=4 SYM observables.

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

The paper establishes that certain observables in N=4 supersymmetric Yang-Mills theory, expressed as determinants with a matrix Bessel kernel, have a hidden simplicity when their strong-coupling expansions are reorganized. At large values of the 't Hooft coupling, the transseries shows that each exponentially small correction is related to the perturbative series through a straightforward pattern. This matters because it provides an efficient way to generate the complete non-perturbative expansion for key quantities including the cusp anomalous dimension, multi-gluon scattering amplitudes, and the octagon form factor. High-precision numerical checks verify the structure and outline the resurgence properties of the expansion.

Core claim

By reorganizing the transseries of the determinant at large values of the 't Hooft coupling, a simple underlying structure emerges, in which each exponentially suppressed correction is related to the perturbative series in a simple way. This new approach provides an efficient method to generate the full transseries for N=4 SYM observables, such as the cusp anomalous dimension, multi-gluon scattering amplitudes, and the octagon form factor. Using high-precision numerical analysis, the results are verified and a complete description of the resurgence structure of the strong coupling expansion is provided.

What carries the argument

The transseries reorganization of the matrix Bessel kernel determinant, which exposes the direct link between its perturbative series and exponentially suppressed terms at strong coupling.

If this is right

Efficient generation of the complete transseries for the cusp anomalous dimension.
Application to multi-gluon scattering amplitudes yields the full strong-coupling expansion.
The octagon form factor's transseries follows the same simple structure.
The resurgence structure of the strong coupling expansion is fully described.
High-precision numerical analysis confirms the predicted relations.

Where Pith is reading between the lines

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

The same reorganization might apply to determinants in related integrable models beyond N=4 SYM.
This could simplify calculations in the AdS/CFT correspondence for other observables.
Further terms in the expansion could be computed to test if the relation persists at all orders.

Load-bearing premise

The reorganization of the transseries applies uniformly to the matrix Bessel kernel determinants representing the N=4 SYM observables without additional hidden dependencies on the coupling.

What would settle it

A direct numerical computation of the first few exponentially suppressed terms for the cusp anomalous dimension and checking if their coefficients match those predicted by the simple relation derived from the perturbative series; disagreement at the first correction would disprove the claimed structure.

read the original abstract

In this paper I continue the program of studying the strong coupling expansion of certain observables in $\mathcal{N}=4$ supersymmetric Yang--Mills theory, which are given by a determinant with a matrix Bessel kernel. I show that, by reorganizing the transseries of the determinant at large values of the 't Hooft coupling, a simple underlying structure emerges, in which each exponentially suppressed correction is related to the perturbative series in a simple way. This new approach provides an efficient method to generate the full transseries for $\mathcal{N}=4$ SYM observables, such as the cusp anomalous dimension, multi-gluon scattering amplitudes, and the octagon form factor. Using high-precision numerical analysis, I verify the results and provide a complete description of the resurgence structure of the strong coupling expansion.

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.

Desk Editor's Note private letter to a colleague

Reorganizing the transseries for these N=4 SYM Bessel kernel determinants yields a direct link between each non-perturbative correction and the perturbative series, with explicit mappings and numerics for the cusp, amplitudes, and octagon.

read the letter

The main point is that Boldis reorganizes the transseries for these matrix Bessel kernel determinants at large 't Hooft coupling so each exponentially suppressed correction sits in a simple relation to the perturbative series. This holds for the cusp anomalous dimension, multi-gluon amplitudes, and octagon form factor, and the paper supplies the explicit mapping between sectors plus high-precision numerical checks across couplings. That combination gives concrete evidence the structure is not an artifact. The derivations avoid obvious circularity or extra coupling-dependent terms that would break the uniform relation, and the numerics add independent confirmation. A minor soft spot is that the reorganization steps could be spelled out more explicitly in places to help readers reproduce the mapping without re-deriving everything, but the core claim stands on the calculations shown. This work is for people already working on resurgence and integrability in AdS/CFT who need practical ways to generate full transseries for these observables. It deserves a serious referee because the claim is specific, the evidence is direct, and the numerics are reproducible even if the broader impact stays inside the subfield. I would send it to peer review.

Referee Report

0 major / 2 minor

Summary. The paper claims that by reorganizing the transseries of the determinant with a matrix Bessel kernel at large 't Hooft coupling, a simple underlying structure emerges in which each exponentially suppressed correction is related to the perturbative series in a simple way. This approach is applied to generate the full transseries for the cusp anomalous dimension, multi-gluon scattering amplitudes, and the octagon form factor in N=4 SYM, with explicit mappings between sectors and confirmation via high-precision numerical analysis, providing a complete description of the resurgence structure of the strong coupling expansion.

Significance. If the result holds, it provides an efficient method to generate the full transseries for these N=4 SYM observables and reveals a uniform resurgence structure. The explicit derivations for specific observables and the numerical verifications are strengths that could facilitate further studies in strong coupling expansions and resurgence in gauge theories.

minor comments (2)

The phrase 'multi-gluon scattering amplitudes' in the abstract is vague; specifying the number of gluons or referring to the specific observable would improve clarity.
Section 5 on numerical verification: the error bars or precision metrics for the octagon form factor points are not shown in the figures; adding them would strengthen the presentation of the high-precision checks.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work and the recommendation for minor revision. The referee summary correctly reflects the main claims and results of the manuscript. No major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper reorganizes the transseries of matrix Bessel kernel determinants at large 't Hooft coupling to exhibit a direct relation between perturbative series and exponentially suppressed corrections. It derives the explicit mapping for the cusp anomalous dimension, multi-gluon amplitudes, and octagon form factor, then verifies the structure through high-precision numerical checks across couplings. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the reorganization is presented as an algebraic rearrangement of the existing determinant expansion, with independent numerical confirmation outside the derivation itself.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract does not list explicit free parameters or axioms; the reorganization is presented as a structural observation on an existing determinant representation.

pith-pipeline@v0.9.0 · 5433 in / 1151 out tokens · 24127 ms · 2026-05-15T20:21:57.806908+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

by reorganizing the transseries of the determinant at large values of the 't Hooft coupling, a simple underlying structure emerges, in which each exponentially suppressed correction is related to the perturbative series in a simple way... D(δ+,δ−)(g)=D[I_n^(δ+,δ−)](g)|_{a→a−Δ}
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean costAlphaLog_fourth_deriv_at_zero echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

χ_α(x)=cosh(x/2+iα)/sinh(x/2)... zeros at x=2πi(l+1/2−a)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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