论文标题
通过Matroid Subdivisions分解广义BIADJOINT标量振幅
Factorization for Generalized Biadjoint Scalar Amplitudes via Matroid Subdivisions
论文作者
论文摘要
我们研究了普遍的双节量表散射幅度残基的问题的问题，$ m^{（k）} _ n $，由Cachazo，早期，Guevara和Mizera（CEGM）引入$ m^{（k）} _ {n_1} \ cdots m^{（k）} _ {n_k} $，其中$ n_1+\ cdots+cdots+n_k = n+k（k-1）$，指出较小的因素是特殊情况。这种行为受到阳性热带草植物中超图像和锥体的常规矩阵细分的几何影响，并由兼容兼容装饰有序的套件的集合（被认为是模量环状旋转）组合。我们针对发生这种情况的条件提出了建议，并详细开发了$ k = 3,4 $。我们简要得出结论，提出了一个新的公式，以构建所有超模拟的最粗糙的常规矩阵细分$δ_{k，n} $和阳性热带草个子的射线，应该具有独立的利益。
We study the problem of factorization for residues of generalized biadjoint scalar scattering amplitudes $m^{(k)}_n$, 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 $m^{(k)}_{n_1}\cdots m^{(k)}_{n_k}$, where $n_1+\cdots +n_k = n+k(k-1)$, 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.
