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arXiv · 2503.15593

The Four-Point Correlator of Planar sYM at Twelve Loops

Jacob L. Bourjaily·Song He·Canxin Shi·Yichao Tang
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Abstract

We determine the 4-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 (22,024,902) 12-loop coefficients; these remaining coefficients can be subsequently fixed using the '(single-)triangle' rule. Not only do we confirm the Catalan conjecture for anti-prism 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 ancillary files to this work.

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Jacob L. Bourjaily, Song He, Canxin Shi, Yichao Tang. 2025-03-19. The Four-Point Correlator of Planar sYM at Twelve Loops. https://arxiv.org/abs/2503.15593

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