论文标题
平面矩阵和Feynman图的阵列：高$ k $的杆
Planar Matrices and Arrays of Feynman Diagrams: Poles for Higher $k$
论文作者
论文摘要
将树图的平面阵列作为Feynman图的概括引入，该图可以使计算biaDjoint振幅$ m^{（k）} _ n $ for $ k> 2 $。在这项后续工作中，我们从此类数组的角度研究了$ m^{（k）} _ n $的电线杆。对于一般的$ k $，我们将基础多层人物描述为标志复合体，并仅根据极点知识来计算振幅的计算，该数字远小于完整阵列的数量。例如，我们首先提供$（k，n）=（3,7），（3,8），（4,8）$和$（4,9）$的所有电线杆。然后，我们将简单的兼容性标准与数组之间的加法操作一起实现，并恢复最近在此类情况下呈现的完整集合/阵列。在此过程中，我们实施了硬和软运动限制，该限制在运动学空间中的两极及其组合阵列之间提供了图。我们使用该操作给出了$（k，n）$和$（n-k，n）$的阵列的先前猜想的组合双重性的证明。我们还概述了与热带Grassmannian $ \ textrm {tr}（k，n）$中的Hypersimplex $δ__{K，N} $的边界图的关系。
Planar arrays of tree diagrams were introduced as a generalization of Feynman diagrams that enables the computation biadjoint amplitudes $m^{(k)}_n$ for $k>2$ . In this follow-up work we investigate the poles of $m^{(k)}_n$ from the perspective of such arrays. For general $k$ we characterize the underlying polytope as a Flag Complex and propose a computation of the amplitude based solely on the knowledge of poles, which number is drastically less than the number of full arrays. As an example we first provide all the poles for the cases $(k,n)=(3,7),(3,8),(4,8)$ and $(4,9)$ in terms of their generalized Feynman diagrams. We then implement a simple compatibility criteria together with an addition operation between arrays, and recover the full collections/arrays recently presented for such cases. Along the way we implement hard and soft kinematical limits, which provide a map between poles in kinematic space and their combinatoric arrays. We use the operation to give a proof of a previously conjectured combinatorial duality for arrays in $(k,n)$ and $(n-k,n)$. We also outline the relation to boundary maps of the hypersimplex $Δ_{k,n}$ and rays in the tropical Grassmannian $\textrm{Tr}(k,n)$.
