Factorization for Generalized Biadjoint Scalar Amplitudes via Matroid Subdivisions

Nick Early

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Submission date: 03. Dec. 2022
Pages: 32
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Abstract:
We study the problem of factorization for residues of generalized biadjoint scalar scattering amplitudes m_n^(k), introduced by Cachazo, Early, Guevara and Mizera (CEGM), involving multi-dimensional residues which factorize generically into k-ary products of lower-point generalized biadjoint amplitudes of the same type m_n1^(k)m_nk^(k), where n₁ + + n_k = n + k(k − 1), noting that smaller numbers of factors arise as special cases. Such behavior is governed geometrically by regular matroid subdivisions of hypersimplices and cones in the positive tropical Grassmannian, and combinatorially by collections of compatible decorated ordered set partitions, considered modulo cyclic rotation. We make a proposal for conditions under which this happens and we develop k = 3,4 in detail. We conclude briefly to propose a novel formula to construct coarsest regular matroid subdivisions of all hypersimplices Δ_k,n and rays of the positive tropical Grassmannian, which should be of independent interest.