We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Centre for Particle Theory

Research Staff

Publication details for Paul Heslop

Heslop, Paul & Stewart, Alastair (2018). The twistor Wilson loop and the amplituhedron. Journal of High Energy Physics 2018(10): 142.

Author(s) from Durham


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.