标题： 双重共形不变运动学与格拉斯曼ian簇代数的折叠 显示英文标题

标题： Dual conformal invariant kinematics and folding of Grassmannian cluster algebras

摘要： In quantum field theory study, Grassmannian manifolds $\text{Gr}(4,n)$ are closely related to $D{=}4$ kinematics input for $n$-particle scattering processes, whose combinatorial and geometrical structures have been widely applied in studying conformal invariant physical theories and their scattering amplitudes. Recently, \cite{HLY21} observed that constraining $D{=}4$ kinematics input to its $D{=}3$ subspace can be interpreted as folding Grassmannian cluster algebras $\mathbb{C}[\text{Gr}(4,n)]$. 在本文中，我们直接从$D{=}3$子空间定义推导出这些约束关于$\text{Gr}(4,n)$的普吕克变量的一般表达式，并提出了一组初始箭图用于代数$\mathbb{C}[\text{Gr}(4,n)]$，其折叠条件正好满足这些约束，从而最终证明了这一观察结果。 显示英文摘要

摘要： In quantum field theory study, Grassmannian manifolds $\text{Gr}(4,n)$ are closely related to $D{=}4$ kinematics input for $n$-particle scattering processes, whose combinatorial and geometrical structures have been widely applied in studying conformal invariant physical theories and their scattering amplitudes. Recently, \cite{HLY21} observed that constraining $D{=}4$ kinematics input to its $D{=}3$ subspace can be interpreted as folding Grassmannian cluster algebras $\mathbb{C}[\text{Gr}(4,n)]$. In this paper, we deduce general expressions for these constraints in terms of Pl\"ucker variables of $\text{Gr}(4,n)$ directly from $D{=}3$ subspace definition, and propose a series of initial quivers for algebra $\mathbb{C}[\text{Gr}(4,n)]$ whose folding conditions exactly meet the constraints, which proves the observation finally.