来自 ABJM 振幅多面体的涌现幺正性、全圈切割与积分
Emergent unitarity, all-loop cuts and integrations from the ABJM amplituhedron
AI总结：
本文研究 ABJM 理论的四点振幅多面体，证明其几何直接给出全圈微扰幺正性和奇数点切割消失，并通过负几何积分提取领头阶尖峰反常维度。
摘要：
我们详细阐述了近期提出的一种新正几何的若干方面，该几何被猜想为 ABJM 理论的四点振幅多面体。我们研究了来自该几何的广义幺正切割，特别证明了：（1）四点被积函数在所有圈均满足微扰幺正性（或光学定理），这直接源于该几何；（2）涉及奇数点振幅的消失切割来自相关“负几何”的“二部”性质，这解释了它们为何出现在 ABJM 理论中。我们还在对这些负几何的形式进行积分方面迈出第一步，并得到一个直到两圈都红外有限的量，从中提取出领头阶的尖峰反常维度。
英文摘要：
We elaborate on aspects of a new positive geometry proposed recently, which was conjectured to be the four-point amplituhedron for ABJM theory. We study generalized unitarity cuts from the geometry, and in particular we prove that (1) the four-point integrand satisfies perturbative unitarity (or optical theorem) to all loops, which follows directly from the geometry, and (2) vanishing cuts involving odd-point amplitudes follow from the ``bipartite" nature of the associated ``negative geometries", which justifies their appearance in ABJM theory. We also take a first step in integrating the forms of these negative geometries and obtain an infrared-finite quantity up to two loops, from which we extract the cusp anomalous dimension at leading order.
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