解开L_{n,k}：格拉斯曼式的Kinnian
Unraveling L_{n,k}: Grassmannian Kinematics
摘要：
最近有人提出N = 4超杨-米尔斯理论的S-矩阵的主要奇点是格拉斯曼流形上围道积分的留数，通过留数定理将柯西定理推广到多个变量来编码时空局部性。我们提供了一种方法来确定对应于任何领先的奇点的残留物，我们进行了非常明确的所有领先的奇点在树级和一个循环。我们还给出了几个例子，在更高的循环，包括所有通用的两个循环领先的奇点和一个有趣的四个循环对象。作为一种特殊情况，我们考虑一个12-pt N^4MHV的前导奇点，它在两个环上有一个新的运动学结构，涉及到双平方根。我们的分析结果在一个简单的图片如何反映在各种子结构内的格拉斯曼圈图的拓扑结构。
英文摘要：
It was recently proposed that the leading singularities of the S-Matrix of N = 4 super Yang-Mills theory arise as the residues of a contour integral over a Grassmannian manifold, with space-time locality encoded through residue theorems generalizing Cauchy's theorem to more than one variable. We provide a method to identify the residue corresponding to any leading singularity, and we carry this out very explicitly for all leading singularities at tree level and one-loop. We also give several examples at higher loops, including all generic two-loop leading singularities and an interesting four-loop object. As a special case we consider a 12-pt N^4MHV leading singularity at two loops that has a new kinematic structure involving double square roots. Our analysis results in a simple picture for how the topological structure of loop graphs is reflected in various substructures within the Grassmannian.
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