Amplituhedron-like geometries

Dian, Gabriele; Heslop, Paul

Abstract

We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of the amplituhedron but with non-maximal winding number. We propose that for the cases with minimal number of points the canonical form of these geometries corresponds to the product of parity conjugate amplitudes at tree as well as loop level. The product of amplitudes in superspace lifts to a star product in bosonised superspace which we give a precise definition of. We give an alternative definition of amplituhedron-like geometries, analogous to the original amplituhedron definition, and also a characterisation as a sum over pairs of on-shell diagrams that we use to prove the conjecture at tree level. The union of all amplituhedron-like geometries has a very simple definition given by only physical inequalities. Although such a union does not give a positive geometry, a natural extension of the standard definition of canonical form, the globally oriented canonical form, acts on this union and gives the square of the amplitude.

Citation

Dian, G., & Heslop, P. (2021). Amplituhedron-like geometries. Journal of High Energy Physics, 2021(11), Article 74. https://doi.org/10.1007/jhep11%282021%29074

• Journal Article Type: Article
• Acceptance Date: Oct 26, 2021
• Online Publication Date: Nov 11, 2021
• Publication Date: 2021
• Deposit Date: Nov 18, 2021
• Publicly Available Date: Nov 26, 2021
• 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: 2021
• Issue: 11
• Article Number: 74
• DOI: https://doi.org/10.1007/jhep11%282021%29074
• Public URL: https://durham-repository.worktribe.com/output/1221289
• Related Public URLs: http://arxiv.org/abs/2106.09372