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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.15593 |
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| _version_ | 1866908275914571776 |
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| author | Bourjaily, Jacob L. He, Song Shi, Canxin Tang, Yichao |
| author_facet | Bourjaily, Jacob L. He, Song Shi, Canxin Tang, Yichao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Four-Point Correlator of Planar sYM at Twelve Loops Bourjaily, Jacob L. He, Song Shi, Canxin Tang, Yichao High Energy Physics - Theory 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. |
| title | The Four-Point Correlator of Planar sYM at Twelve Loops |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.15593 |