标题： CEGM NLSM 显示英文标题

标题： The CEGM NLSM

摘要： 通过几何原理研究量子场论揭示了物理与数学之间的深刻联系，包括Cachazo、Early、Guevara和Mizera（CEGM）发现的双伴随标量振幅的推广。然而，将这一成果扩展到其他量子场论的推广仍然是一个核心挑战。最近发现，非线性σ模型（NLSM）在某种保持零点的变形后从$\text{tr}(\phi^3)$出现。在本工作中，我们在CEGM背景下发现了保持零点变形的更丰富的故事，得到了广义的NLSM振幅。我们证明了一个显式公式，用于$n$点NLSM振幅在混合$n+2$点广义NLSM振幅中的残余嵌入，这为我们提出的推广提供了强有力的自洽性检验。我们表明纯运动学变形空间的维数是$\gcd(k,n)-1$，我们引入了一种与变形兼容的全局施温格参数化修改，并且我们使用拟阵刀片排列的方法，给出了CEGM振幅中平面运动学不变量集的线性独立性的新证明。我们的框架通过最近对Koba-Nielsen弦积分在任何正配置空间$X^+(k,n)$的推广而与弦理论相容，其中通常的Koba-Nielsen弦积分对应于$X(2,n) = \mathcal{M}_{0,n}$。 显示英文摘要

摘要： Studying quantum field theories through geometric principles has revealed deep connections between physics and mathematics, including the discovery by Cachazo, Early, Guevara and Mizera (CEGM) of a generalization of biadjoint scalar amplitudes. However, extending this to generalizations of other quantum field theories remains a central challenge. Recently it has been discovered that the nonlinear sigma model (NLSM) emerges after a certain zero-preserving deformation from $\text{tr}(\phi^3)$. In this work, we find a much richer story of zero-preserving deformations in the CEGM context, yielding generalized NLSM amplitudes. We prove an explicit formula for the residual embedding of an $n$-point NLSM amplitude in a mixed $n+2$ point generalized NLSM amplitude, which provides a strong consistency check on our generalization. We show that the dimension of the space of pure kinematic deformations is $\gcd(k,n)-1$, we introduce a deformation-compatible modification of the Global Schwinger Parameterization, and we include a new proof, using methods from matroidal blade arrangements, of the linear independence for the set of planar kinematic invariants for CEGM amplitudes. Our framework is compatible with string theory through recent generalizations of the Koba-Nielsen string integral to any positive configuration space $X^+(k,n)$, where the usual Koba-Nielsen string integral corresponds to $X(2,n) = \mathcal{M}_{0,n}$.