正交动量振幅面和ABJM振幅
The orthogonal momentum amplituhedron and ABJM amplitudes
摘要：
本文介绍了ABJM理论中三能级散射振幅的动量空间振幅面。我们证明了散射振幅可以被识别为正正交格拉斯曼和矩曲线的乘积所给出的空间上的标准形。这个空间的余维1边界仅仅是奇数粒子的平面曼德尔维变量，而偶数粒子的对应物被“隐藏”为更高的余维边界。值得注意的是，这个空间同样可以通过一系列“符号翻转”的要求，预计外部数据，相同的“一半”四维$\mathcal{N}=4$超级杨米尔斯理论（sYM）。因此，在精确意义上，ABJM的几何形状位于$\mathcal{N}=4$ sYM的边界上。我们通过八个点验证了这种关系，表明振幅的BCFW三角剖分瓦片的振幅面体。在ABJM理论的$\mathcal{N}=4$形式体系中，使用格拉斯曼振幅公式自然导出标准形式。
英文摘要：
In this paper, we introduce the momentum space amplituhedron for tree-level scattering amplitudes of ABJM theory. We demonstrate that the scattering amplitude can be identified as the canonical form on the space given by the product of positive orthogonal Grassmannian and the moment curve. The co-dimension one boundaries of this space are simply the odd-particle planar Mandelstam variables, while the even-particle counterparts are "hidden" as higher co-dimension boundaries. Remarkably, this space can be equally defined through a series of "sign flip" requirements of the projected external data, identical to "half" of four-dimensional $\mathcal{N}=4$ super Yang-Mills theory (sYM). Thus in a precise sense the geometry for ABJM lives on the boundary of $\mathcal{N}=4$ sYM. We verify this relation through eight-points by showing that the BCFW triangulation of the amplitude tiles the amplituhedron. The canonical form is naturally derived using the Grassmannian formula for the amplitude in the $\mathcal{N}=4$ formalism for ABJM theory.
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