杨-米尔斯关联函数的正几何
Positive Geometry of Yang-Mills Correlators
AI总结：
该研究通过宇宙格拉斯曼流形的正几何表述，构建了德西特空间中三点、四点树级杨-米尔斯关联函数，结合同调表述重现了完整四点结果，为更高点宇宙学关联函数的几何描述提供了起点。
AI中文摘要：
我们通过宇宙格拉斯曼流形上的 helicity 剥离表示，建立了德西特空间中三点和四点树级杨-米尔斯关联函数的正几何表述。在其 Pfaffian（或旋量）嵌入中，物理奇点成为自然的几何边界。对于三点情况，杨-米尔斯关联函数是格拉斯曼流形中非负卦限的典范形式；对于四点情况，曼德尔施塔姆除子将格拉斯曼流形的 Pfaffian 正域划分为四个正几何。要求其可因式分解为三点形式并满足正确的平直空间极限，唯一地选出这些区域中两个区域的定向并集，其典范形式可重现约化的颜色有序杨-米尔斯关联函数。而完整的颜色有序关联函数则由同调环的唯一确定的带符号线性组合产生。因此，正几何的更广泛同调表述对于获取完整的四点结果至关重要。我们的构造为更高点宇宙学关联函数的几何描述提供了具体的起点。
英文摘要：
We develop a positive-geometric formulation of tree-level Yang-Mills correlators in de Sitter space at three and four points through their helicity-stripped representatives on the cosmological Grassmannian. In its Pfaffian (or spinor) embedding, physical singularities become natural geometric boundaries. At three points, the Yang-Mills correlator is the canonical form of the non-negative orthant in the Grassmannian. At four points, the Mandelstam divisors partition the Pfaffian-positive domain of the Grassmannian into four positive geometries. Requiring factorization into three-point forms, together with the correct flat-space limit, uniquely selects an oriented union of two of these regions, whose canonical form reproduces the reduced color-ordered Yang-Mills correlator. The full color-ordered correlator, on the other hand, arises from a uniquely fixed signed linear combination of homology cycles. Thus, the broader homological formulation of positive geometry is essential for capturing the complete four-point result. Our construction provides a concrete starting point for a geometric description of higher-point cosmological correlators.
