The twistor Wilson loop and the amplituhedron

Heslop, Paul; Stewart, Alastair

Abstract

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.

Citation

Heslop, P., & Stewart, A. (2018). The twistor Wilson loop and the amplituhedron. Journal of High Energy Physics, 2018(10), Article 142. https://doi.org/10.1007/jhep10%282018%29142

• 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
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2018
• Issue: 10
• Article Number: 142
• DOI: https://doi.org/10.1007/jhep10%282018%29142
• Public URL: https://durham-repository.worktribe.com/output/1314583