论文标题
关于KLT关系的多面体和概括
On Polytopes and Generalizations of the KLT Relations
论文作者
论文摘要
我们结合了多面体理论和扭曲的交叉理论的技术，以得出大量的双重复制关系，这些关系概括了由于Kawai，Lewellen和Tye（KLT）而引起的经典关系。为此，我们首先研究了Cachazo，他和Yuan的散射方程的概括。虽然散射方程是在$ \ Mathcal {M} _ {0，N} $上定义的 - 标记的Riemann球体的模量空间 - 新的散射方程是在已知的AccountioHedra上定义的，被称为AccordioHedra，被认为是增生平面布置。这些多面体编码为相交的模式，即通用标量理论的散射幅度。此类交叉点的扭曲时期关系提供了KLT关系的广泛概括。超平面布置的有界腔室的差分形式提供了伯尔尼 - 卡拉斯科 - 约翰逊（BCJ）基础的自然概括，可以通过计算广义散射方程的溶液数量来确定其数量。在这项工作中，重点是将BCJ扩展到通用标量理论的概括，尽管我们可以互换使用标签KLT和BCJ。
We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT) . To do this, we first study a generalization of the scattering equations of Cachazo, He and Yuan. While the scattering equations were defined on $\mathcal{M}_{0,n}$ - the moduli space of marked Riemann spheres - the new scattering equations are defined on polytopes known as accordiohedra, realized as hyperplane arrangements. These polytopes encode as patterns of intersection the scattering amplitudes of generic scalar theories. The twisted period relations of such intersection numbers provide a vast generalization of the KLT relations. Differential forms dual to the bounded chambers of the hyperplane arrangements furnish a natural generalization of the Bern-Carrasco-Johansson (BCJ) basis, the number of which can be determined by counting the number of solutions of the generalized scattering equations. In this work the focus is on a generalization of the BCJ expansion to generic scalar theories, although we use the labels KLT and BCJ interchangeably.
