论文标题
非平面BCFW Grassmannian几何形状
Non-planar BCFW Grassmannian Geometries
论文作者
论文摘要
在本文中，我们研究了非高雅的BCFW递归关系及其与阳性几何形状的联系。对于相邻的BCFW偏移，$ n $ -point n $^k $ MHV树级幅度$ {\ cal n} = 4 $ sym理论表示为平面上的壳图上的总和，对应于阳性Grassmannian $ g _+（k，k，k，n）$。非粘量BCFW自然会以不同的对象的形式移动振幅的扩展，这些对象没有表现出循环排序和振幅的隐藏对称性。我们表明，这些术语可以解释为在非平面格拉曼尼亚几何形状上的dlog形式，将阳性的格拉斯曼尼亚$ g _+（k，n）$的细胞推广到生活在$ g（k，n）$中的较大类别的对象上。我们主要关注NMHV振幅的情况，并详细讨论Grassmannian几何形状。我们还提出了一种替代方法，以使用格拉曼尼亚构型与运动学空间中的几何形状之间的有趣联系来计算相关的壳函数和DLOG形式。
In this paper, we study non-adjacent BCFW recursion relations and their connection to positive geometry. For an adjacent BCFW shift, the $n$-point N$^k$MHV tree-level amplitude in ${\cal N}=4$ SYM theory is expressed as a sum over planar on-shell diagrams, corresponding to canonical dlog forms on the cells in the positive Grassmannian $G_+(k,n)$. Non-adjacent BCFW shifts naturally lead to an expansion of the amplitude in terms of a different set of objects, which do not manifest the cyclic ordering and the hidden Yangian symmetry of the amplitude. We show that these terms can be interpreted as dlog forms on the non-planar Grassmannian geometries, generalizing the cells of the positive Grassmannian $G_+(k,n)$ to a larger class of objects which live in $G(k,n)$. We focus mainly on the case of NMHV amplitudes and discuss in detail the Grassmannian geometries. We also propose an alternative way to calculate the associated on-shell functions and dlog forms using an intriguing connection between Grassmannian configurations and the geometry in the kinematical space.
