论文标题
热带风扇，散射方程和振幅
Tropical fans, scattering equations and amplitudes
论文作者
论文摘要
我们描述了一个与格拉斯曼群岛代数有关的热带迷。这些风扇在多种方面与无质量散射过程的运动学空间有关。对于与Grassmannian $ {\ rm gr}（k，n）$相关的每个风扇，都有一个广义的$ ϕ^3 $振幅和一组相关的散射方程式，这些方程式进一步推广了$ {\ rm gr}（k，n）$散射方程。在这里，我们主要关注与有限的硕士群集代数相关的案例，我们解释了群集多面体的面部变量如何与散射方程式有关。对于Grassmannians $ {\ rm gr}（4，n）$，我们描述的热带迷与平面$ \ Mathcal {n} = 4 $ Super Yang-Mills理论的环路振幅的奇异性（或符号字母）有关。我们展示了热带风扇的每种选择如何导致一类天然的小聚集体，从而概括了聚类邻接的概念，并描述了当前已知的环路数据如何拟合到该分类中。
We describe a family of tropical fans related to Grassmannian cluster algebras. These fans are related to the kinematic space of massless scattering processes in a number of ways. For each fan associated to the Grassmannian ${\rm Gr}(k,n)$ there is a notion of a generalised $ϕ^3$ amplitude and an associated set of scattering equations which further generalise the ${\rm Gr}(k,n)$ scattering equations that have been recently introduced. Here we focus mostly on the cases related to finite Grassmannian cluster algebras and we explain how face variables for the cluster polytopes are simply related to the scattering equations. For the Grassmannians ${\rm Gr}(4,n)$ the tropical fans we describe are related to the singularities (or symbol letters) of loop amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory. We show how each choice of tropical fan leads to a natural class of polylogarithms, generalising the notion of cluster adjacency and we describe how the currently known loop data fit into this classification.
