Unwinding the amplituhedron in binary
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Publication:1745430
DOI10.1007/JHEP01(2018)016zbMATH Open1384.81130arXiv1704.05069OpenAlexW3106166312MaRDI QIDQ1745430
Author name not available (Why is that?)
Publication date: 17 April 2018
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/1704.05069
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