论文标题
动量Amplituhedron遇到运动学相关
Momentum Amplituhedron meets Kinematic Associahedron
论文作者
论文摘要
在本文中，我们研究了两种积极几何形状之间的关系：动量扩增子，与$ \ Mathcal {n} = 4 $ Super Yang-Mills理论和运动型相关型相关的树级散射幅度有关我们研究了将后者限制为四个时空维度的含义，并在其规范形式与动量Amplituhedron的规范形式之间提供直接联系。在删除了量规理论的小组缩放依赖性之后，我们发现我们可以将所得的还原形式与AssociaHedron形式的背包进行比较。特别是，相关形式是减少动量扩增子形式的所有螺旋扇区的总和。这种关系突出了各个幅度的共同奇异性结构。特别是，分解通道对应于消失的平面mandelstam变量，是相同的。此外，当通过克决定性约束降低到四个时空维度时，我们还直接在标量理论的运动学空间上找到了这些规范形式之间的关系。作为我们工作的副产品，我们提供了与四维规格和标量理论相关的运动空间的详细分析，并提供了它们之间的直接联系。
In this paper we study a relation between two positive geometries: the momentum amplituhedron, relevant for tree-level scattering amplitudes in $\mathcal{N} = 4$ super Yang-Mills theory, and the kinematic associahedron, encoding tree-level amplitudes in bi-adjoint scalar $ϕ^3$ theory. We study the implications of restricting the latter to four spacetime dimensions and give a direct link between its canonical form and the canonical form for the momentum amplituhedron. After removing the little group scaling dependence of the gauge theory, we find that we can compare the resulting reduced form with the pull-back of the associahedron form. In particular, the associahedron form is the sum over all helicity sectors of the reduced momentum amplituhedron forms. This relation highlights the common singularity structure of the respective amplitudes; in particular the factorization channels, corresponding to vanishing planar Mandelstam variables, are the same. Additionally, we also find a relation between these canonical forms directly on the kinematic space of the scalar theory when reduced to four spacetime dimensions by Gram determinant constraints. As a by-product of our work we provide a detailed analysis of the kinematic spaces relevant for the four-dimensional gauge and scalar theories, and provide direct links between them.
