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The twistor Wilson loop and the amplituhedron

Heslop, Paul; Stewart, Alastair

The twistor Wilson loop and the amplituhedron Thumbnail


Alastair Stewart


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.


Heslop, P., & Stewart, A. (2018). The twistor Wilson loop and the amplituhedron. Journal of High Energy Physics, 2018(10), Article 142.

Journal Article Type Article
Acceptance Date Oct 14, 2018
Online Publication Date Oct 23, 2018
Publication Date Oct 23, 2018
Deposit Date Nov 8, 2018
Publicly Available Date Nov 8, 2018
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2018
Issue 10
Article Number 142


Published Journal Article (458 Kb)

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Copyright 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.

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