Scattering equations and Kawai-Lewellen-Tye orthogonality
Scattering equations and Kawai-Lewellen-Tye orthogonality
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DOI：
10.1103/physrevd.90.065001
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发表时间：
2014-09-03
影响因子：
5
通讯作者：
Yuan, Ellis Ye
中科院分区：
文献类型：
--
作者：
Cachazo, Freddy;He, Song;Yuan, Ellis Ye
最近的一些发展指出，从n-穿孔球到D维动量空间零锥的有理映射为描述D维无质量粒子的散射提供了一种自然的语言。在本文中，我们确定和研究方程的运动学不变量s（ab）和穿刺位置σ（c），我们称之为散射方程。我们提供了一个归纳算法的粒子数为他们的解决方案，并证明了显着的性质，我们称之为Kawai-Lewellen-Tye（KLT）正交。简而言之，KLT正交性意味着从散射方程的解构造的“Parke-Taylor”向量关于KLT双线性形式相互正交。最后，我们评论可能的连接规范理论和重力振幅在任何维度和高能量极限弦理论振幅。
Several recent developments point to the fact that rational maps from n-punctured spheres to the null cone of D-dimensional momentum space provide a natural language for describing the scattering of massless particles in D dimensions. In this paper we identify and study equations relating the kinematic invariants s(ab) and the puncture locations sigma(c), which we call the scattering equations. We provide an inductive algorithm in the number of particles for their solutions and prove a remarkable property which we call Kawai-Lewellen-Tye (KLT) orthogonality. In a nutshell, KLT orthogonality means that "Parke-Taylor" vectors constructed from the solutions to the scattering equations are mutually orthogonal with respect to the KLT bilinear form. We end with comments on possible connections to gauge theory and gravity amplitudes in any dimension and to the high-energy limit of string theory amplitudes.