论文标题
无穷大的波线在壳图中
Poles At Infinity in On-shell Diagrams
论文作者
论文摘要
在本文中，我们研究了$ {\ cal n} {<} 4 $超对称Yang-Mills（Sym）理论的壳图。这些是壳体仪表不变的对象，在广义单位性的背景下是循环集成的切割，并用作递归关系中振幅的构件。在双重公式中，它们与阳性Grassmannian $ g _+（k，n）$的细胞相关，并且可以将壳函数重现为规范的差分形式。 While for the case of the ${\cal N}{=}4$ maximally supersymmetric Yang-Mills theory all poles in on-shell diagrams correspond to IR poles when the momentum flows in edges are zero, for ${\cal N}{<}4$ SYM theories there are new UV poles when the loop momenta go to infinity.这些极点源于规范dlog形式的预成分，与壳图中的擦除边缘不相对应。我们证明它们可以解释为一种示意操作，涉及捏合循环并在外腿上执行``非平面扭曲''，这会导致非平面壳图。我们的结果为极点在无限动量振幅中的作用以及与非平面上壳上函数的关系提供了重要的线索。
In this paper we study on-shell diagrams in ${\cal N}{<}4$ supersymmetric Yang-Mills (SYM) theory. These are on-shell gauge invariant objects which appear as cuts of loop integrands in the context of generalized unitarity and serve as building blocks for amplitudes in recursion relations. In the dual formulation, they are associated with cells of the positive Grassmannian $G_+(k,n)$ and the on-shell functions can be reproduced as canonical differential forms. While for the case of the ${\cal N}{=}4$ maximally supersymmetric Yang-Mills theory all poles in on-shell diagrams correspond to IR poles when the momentum flows in edges are zero, for ${\cal N}{<}4$ SYM theories there are new UV poles when the loop momenta go to infinity. These poles originate from the prefactor of the canonical dlog form and do not correspond to erasing edges in on-shell diagrams. We show that they can be interpreted as a diagrammatic operation which involves pinching a loop and performing a ``non-planar twist'' on external legs, which gives rise to a non-planar on-shell diagram. Our result provides an important clue on the role of poles at infinite momenta in on-shell scattering amplitudes, and the relation to non-planar on-shell functions.
