论文标题
循环amplituhedron的内边界
Internal boundaries of the loop amplituhedron
论文作者
论文摘要
正面几何形状的严格定义意味着其规范形式的所有最大残基均为$ \ pm 1 $。但是，我们观察到，平面$ \ MATHCAL {n} = 4 $ SUPER YANG-MILLS中的振幅的循环集成具有最大残基不等于$ \ pm 1 $。我们发现这样做的原因是，在循环扩展的边界结构中，有几何形状包含内部边界：编纂的一个缺陷将两个相反方向的区域分开。这种现象需要对积极几何形状和规范形式的概念进行概括，以包括这种内部边界，还表明了对“加权阳性几何形状”的进一步概括的实用性。我们对$ \ Mathcal {n} = 4 $振幅的最深切割重新检查，并获得新的所有订单残留物。
The strict definition of positive geometry implies that all maximal residues of its canonical form are $\pm 1$. We observe, however, that the loop integrand of the amplitude in planar $\mathcal{N}=4$ super Yang-Mills has maximal residues not equal to $\pm 1$. We find the reason for this is that deep in the boundary structure of the loop amplituhedron there are geometries which contain internal boundaries: codimension one defects separating two regions of opposite orientation. This phenomenon requires a generalisation of the concept of positive geometry and canonical form to include such internal boundaries and also suggests the utility of a further generalisation to `weighted positive geometries'. We re-examine the deepest cut of $\mathcal{N}=4$ amplitudes in light of this and obtain new all order residues.
