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The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM

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arxiv 2001.05460 v2 pith:OYHNXHGD submitted 2020-01-15 hep-th

Benjamin Basso , Lance J. Dixon , Georgios Papathanasiou This is my paper · ORCID
classification hep-th
keywords couplinganomalousdimensionsamplitudecrossmathcalplanarratios
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We study the maximally-helicity-violating (MHV) six-gluon scattering amplitude in planar $\mathcal{N} = 4$ super-Yang-Mills theory at finite coupling when all three cross ratios are small. It exhibits a double logarithmic scaling in the cross ratios, controlled by a handful of "anomalous dimensions" that are functions of the coupling constant alone. Inspired by known seven-loop results at weak coupling and the integrability-based pentagon OPE, we present conjectures for the all-order resummation of these anomalous dimensions. At strong coupling, our predictions agree perfectly with the string theory analysis. Intriguingly, the simplest of these anomalous dimensions coincides with one describing the light-like limit of the octagon, namely the four-point function of large-charge BPS operators.

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Cited by 4 Pith papers

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

  1. Lattice path combinatorics in superconformal Yang-Mills theories

    hep-th 2025-08 conditional novelty 8.0 of 10

    Planar superconformal Yang-Mills determinant observables are shown to equal generalized Dyck path partition functions through a universal iterated integral expansion.

  2. Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons

    hep-th 2025-12 conditional novelty 7.0 of 10

    A general two-loop formula is obtained for all n-point 10d null polygon correlators in planar N=4 SYM, expressed in a conformal-integral basis and verified numerically at 11 points.

  3. From Fredholm Determinants to AdS/CFT Observables: A Universal Strong-Coupling Framework

    hep-th 2026-07 conditional novelty 6.0 of 10

    The O(6) mass gap's strong-coupling trans-series is generated from Fredholm-determinant data via a conjectured alien calculus, yielding an all-orders relation to the cusp anomalous dimension.

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

    hep-th 2026-02 unverdicted novelty 6.0 of 10

    The strong-coupling transseries for matrix Bessel determinant observables is generated from its perturbative part by shifting a→a−Δ and replacing moments I_n, with all Stokes constants fixed by two recurrences.

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