Serendipitous Syzygies of Scattering Amplitudes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915295599263744 |
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| author | Kosower, David A. Pögel, Sebastian |
| author_facet | Kosower, David A. Pögel, Sebastian |
| contents | We study linear relations between color-ordered all-plus amplitudes at one loop in Yang--Mills theory. We show that on general grounds, there are $(n-1)!/2-2$ relations for $n\ge 5$, leaving only two independent color-ordered amplitudes. We present two complementary approaches to finding such relations: one using numerical linear algebra and the other using syzygies in computational algebraic geometry. We obtain explicit forms for all relations through $n=7$. We also study relations for the tree-level MHV amplitudes through $n=8$. The latter relations include the well-known color and Bern--Carrasco--Johansson identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Serendipitous Syzygies of Scattering Amplitudes Kosower, David A. Pögel, Sebastian High Energy Physics - Theory High Energy Physics - Phenomenology We study linear relations between color-ordered all-plus amplitudes at one loop in Yang--Mills theory. We show that on general grounds, there are $(n-1)!/2-2$ relations for $n\ge 5$, leaving only two independent color-ordered amplitudes. We present two complementary approaches to finding such relations: one using numerical linear algebra and the other using syzygies in computational algebraic geometry. We obtain explicit forms for all relations through $n=7$. We also study relations for the tree-level MHV amplitudes through $n=8$. The latter relations include the well-known color and Bern--Carrasco--Johansson identities. |
| title | Serendipitous Syzygies of Scattering Amplitudes |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2505.14857 |