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Four-point correlator of planar supersymmetric Yang-Mills theory at twelve loops

Jacob L. Bourjaily1,*, Song He (何颂)2,3,†, Canxin Shi (施灿欣)2,‡, and Yichao Tang (唐一朝)2,4,§

  • *Contact author: bourjaily@psu.edu
  • †Contact author: songhe@itp.ac.cn
  • ‡Contact author: shicanxin@itp.ac.cn
  • §Contact author: tangyichao@itp.ac.cn
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Phys. Rev. D 112, 126029 – Published 31 December, 2025

DOI: https://doi.org/10.1103/kl4q-mpwp

Abstract

We determine the four-point correlation function and amplitude in planar, maximally supersymmetric Yang-Mills theory to 12 loops. We find that the recently introduced “double-triangle” rule in fact implies the previously described square and pentagon rules; and when applied to 12 loops, it fully determines the 11-loop correlator and fixes all but 3 of the (619,981,403) 12-loop coefficients; these remaining coefficients can be subsequently fixed using the “(single-)triangle” rule. Not only do we confirm the Catalan conjecture for antiprism graphs, but we discover evidence for a greatly generalized Catalan conjecture for the coefficients of all polygon-framed fishnet graphs. We provide all contributions through 12 loops as Supplemental Material to this work.

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Supplemental Material

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Outline

Information

Phys. Rev. D 112, 126029– Published 31 December, 2025
  • Received 26 March 2025
  • Accepted 14 November 2025
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