Amplituhedron-like geometries

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...

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Autores principales:	Gabriele Dian, Paul Heslop
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Scattering Amplitudes Supersymmetric Gauge Theory Conformal Field Theory Extended Supersymmetry Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/7f69f0a57613457dad455940b2e8b504
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id	oai:doaj.org-article:7f69f0a57613457dad455940b2e8b504
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spelling	oai:doaj.org-article:7f69f0a57613457dad455940b2e8b5042021-11-14T12:41:08ZAmplituhedron-like geometries10.1007/JHEP11(2021)0741029-8479https://doaj.org/article/7f69f0a57613457dad455940b2e8b5042021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)074https://doaj.org/toc/1029-8479Abstract 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.Gabriele DianPaul HeslopSpringerOpenarticleScattering AmplitudesSupersymmetric Gauge TheoryConformal Field TheoryExtended SupersymmetryNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-54 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Scattering Amplitudes Supersymmetric Gauge Theory Conformal Field Theory Extended Supersymmetry Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Scattering Amplitudes Supersymmetric Gauge Theory Conformal Field Theory Extended Supersymmetry Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Gabriele Dian Paul Heslop Amplituhedron-like geometries
description	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.
format	article
author	Gabriele Dian Paul Heslop
author_facet	Gabriele Dian Paul Heslop
author_sort	Gabriele Dian
title	Amplituhedron-like geometries
title_short	Amplituhedron-like geometries
title_full	Amplituhedron-like geometries
title_fullStr	Amplituhedron-like geometries
title_full_unstemmed	Amplituhedron-like geometries
title_sort	amplituhedron-like geometries
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/7f69f0a57613457dad455940b2e8b504
work_keys_str_mv	AT gabrieledian amplituhedronlikegeometries AT paulheslop amplituhedronlikegeometries
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Amplituhedron-like geometries

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