源自正几何的规范性幺正性
Prescriptive Unitarity from Positive Geometries
AI总结：
本文在对偶动量的四维分裂符号空间中定义了动量Amplituhedron，利用该几何的规范微分形式推导出N=4超Yang-Mills的单圈振幅积分核新公式，并证明其与prescriptive unitarity结果一致，使该幺正性方法自然涌现。
摘要：
在本文中，我们在对偶动量的四维分裂符号空间中定义了动量Amplituhedron。它在平面扇区内编码了N=4超Yang-Mills的树级散射振幅和圈积分核。在此描述中，树级几何中的每个点由一个零多边形指定。利用该运动学空间的零结构，我们找到了一个几何，其规范微分形式产生了圈振幅积分核。值得注意的是，在单圈时它是简单多面体的弯曲版本，其顶点由振幅的极大割指定。这一构造使我们能够为任意多重性和螺旋度的振幅找到单圈积分核的新公式。以这种方式获得的公式与通过prescriptive unitarity推导出的公式一致。这使得prescriptive unitarity从这一几何描述中自然涌现。
英文摘要：
In this paper, we define the momentum amplituhedron in the four-dimensional split-signature space of dual momenta. It encodes scattering amplitudes at tree level and loop integrands for N=4 super Yang-Mills in the planar sector. In this description, every point in the tree-level geometry is specified by a null polygon. Using the null structure of this kinematic space, we find a geometry whose canonical differential form produces loop-amplitude integrands. Remarkably, at one loop it is a curvy version of a simple polytope, whose vertices are specified by maximal cuts of the amplitude. This construction allows us to find novel formulae for the one-loop integrands for amplitudes with any multiplicity and helicity. The formulae obtained in this way agree with the ones derived via prescriptive unitarity. It makes prescriptive unitarity naturally emerge from this geometric description.
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