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The twistor Wilson loop and the amplituhedron.

Heslop, Paul and Stewart, Alastair (2018) 'The twistor Wilson loop and the amplituhedron.', Journal of high energy physics., 2018 (10). p. 142.


The amplituhedron provides a beautiful description of perturbative superamplitude integrands in N = 4 SYM in terms of purely geometric objects, generalisations of polytopes. On the other hand the Wilson loop in supertwistor space also gives an explicit description of these superamplitudes as a sum of planar Feynman diagrams. Each Feynman diagram can be naturally associated with a geometrical object in the same space as the amplituhedron (although not uniquely). This suggests that these geometric images of the Feynman diagrams give a tessellation of the amplituhedron. This turns out to be the case for NMHV amplitudes. We argue however that beyond NMHV this is not true. Specifically, each Feynman diagram leads to an image with a physical boundary and spurious boundaries. The spurious ones should be “internal”, matching with neighbouring diagrams. We however show that there is no choice of geometric image of the Wilson loop Feynman diagrams which yields a geometric object without leaving unmatched spurious boundaries.

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Publisher statement:This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:14 October 2018
Date deposited:08 November 2018
Date of first online publication:23 October 2018
Date first made open access:No date available

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