二进制中的振幅面体展开
Unwinding the Amplituhedron in Binary
摘要：
我们提出了新的，从根本上组合和拓扑特征的振幅面体。在通过振幅面体投影外部数据时，所得到的点的配置具有指定的（和最大的）广义“缠绕数”。同样，振幅面体可以完全用二进制描述：几何体向下到一维的规范投影具有投影数据的指定（和最大）数量的“符号翻转”。散射振幅的局域性和么正性很容易作为这个二进制码的基本结果导出。最小缠绕定义了振幅面体的自然“对偶”。这幅图给了我们一个振幅面体在矢量空间（物理学中的动量扭量空间）中点位形空间中的化身，一个正则振幅面体形式的新解释，以及一个作为物理运动学数据空间上的微分形式的平面N = 4 SYM中散射超振幅的直接玻色子理解。
英文摘要：
We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized 'winding number'. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of 'sign flips' of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines a natural 'dual' of the amplituhedron. This picture gives us an avatar of the amplituhedron purely in the configuration space of points in vector space (momentum-twistor space in the physics), a new interpretation of the canonical amplituhedron form, and a direct bosonic understanding of the scattering super-amplitude in planar N = 4 SYM as a differential form on the space of physical kinematical data.
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