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Serendipitous syzygies of scattering amplitudes
Phys. Rev. D 112, 076030 – Published 23 October, 2025
DOI: https://doi.org/10.1103/cypj-74sj
Abstract
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 relations for , 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 . We also study relations for the tree-level maximally helicity violating amplitudes through . The latter relations include the well-known color and Bern-Carrasco-Johansson identities.
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