发表机构
Indian Institute of Science Education and Research, Pune（印度科学教育与研究学院浦那分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出标量生成势方法，在正交格拉斯曼空间中统一计算任意自旋四点宇宙学关联函数，实现胶子与引力子的微分双拷贝，并揭示颜色恒等式的射影几何起源。
AI 中文摘要
我们引入了新颖的标量生成势，用于在正交格拉斯曼空间中计算三点和四点宇宙学关联函数。这些关联函数通过对这些势施加适当的方向导数，并结合依赖于螺旋度的小子式来获得。我们强调，这不是自旋提升的类比，而是一个更强大的构造。四点生成势与射影三角形的几何相关联。一阶方向导数生成胶子关联函数，而同一标量势的Hessian矩阵则产生四引力子关联函数，从而实现了一个微分形式的双拷贝。因此，双拷贝是作为胶子和引力子四点关联函数起源的底层标量势的自然结果。该框架自然地扩展到任意自旋$s$。我们展示了胶子颜色恒等式的几何起源：标量势的射影齐次性蕴含了Kleiss-Kuijf恒等式，而运动学Jacobi恒等式则作为三角形在方向导数下闭合的结果而得出。我们还揭示了BCFW桥变形与产生自旋$s$关联函数的方向导数之间的联系。因此，生成势为任意自旋$s$的四点格拉斯曼关联函数提供了一个普遍的几何解释，这与文献[Bala:2026lvw]不同，后者仅对胶子展示了几何解释。
英文摘要
We introduce novel scalar generating potentials to compute three and four point cosmological correlators in orthogonal Grassmannian space. These correlators are obtained by applying appropriate directional derivatives on these potentials, combined with helicity-dependent minors. We emphasize that, this is not a spin-raising analog, but a much more powerful construction. The four point generating potential is associated with the geometry of a projective triangle. First-order directional derivatives generate gluon correlator, while the Hessian of the same scalar potential produces the four-graviton correlators, thus realizing a differential double copy. Thus, double copy is a natural consequence of the underlying scalar potential as the origin of the gluon and graviton four point correlators. This framework extends naturally to any spin-$s$. We exhibit a geometric origin for the gluon colour identities: the projective homogeneity of the scalar potential implies Kleiss-Kuijf identity, while the kinematic Jacobi identity follows as a consequence of the closure of the triangle under directional derivatives. We also uncover a connection between the BCFW bridge deformation of the scalar potential and directional derivatives that produces the spin-s correlator. Thus the generating potential provides a universal geometrical interpretation for any spin-$s$ four point Grassmannian correlator, unlike \cite{Bala:2026lvw} where geometric interpretation was only shown for the gluons.
Comments6 pages, 1 figure. Comments are welcome
