Tropical fans, scattering equations and amplitudes
Tropical fans, scattering equations and amplitudes
We describe a family of tropical fans related to Grassmannian cluster algebras. These fans are related to the kinematic space of massless scattering processes in a number of ways. For each fan associated to the Grassmannian Gr(k, n) there is a notion of a generalised ϕ3 amplitude and an associated set of scattering equations which further generalise the Gr(k, n) scattering equations that have been recently introduced. Here we focus mostly on the cases related to finite Grassmannian cluster algebras and we explain how face variables for the cluster polytopes are simply related to the scattering equations. For the Grassmannians Gr(4, n) the tropical fans we describe are related to the singularities (or symbol letters) of loop amplitudes in planar
= 4 super Yang-Mills theory. We show how each choice of tropical fan leads to a natural class of polylogarithms, generalising the notion of cluster adjacency and we describe how the currently known loop data fit into this classification.
Drummond, James
3ea15544-457f-4e72-8ad0-60f3136841db
Foster, Jack
375960ff-578f-4309-93ef-4c55cecf76d2
Gürdoğan, Ömer
841de8b6-4eb2-407f-a4c4-c8136403794d
Kalousios, Chrysostomos
bb47cef9-3c7c-4108-99cb-9e80cd8ed704
10 November 2021
Drummond, James
3ea15544-457f-4e72-8ad0-60f3136841db
Foster, Jack
375960ff-578f-4309-93ef-4c55cecf76d2
Gürdoğan, Ömer
841de8b6-4eb2-407f-a4c4-c8136403794d
Kalousios, Chrysostomos
bb47cef9-3c7c-4108-99cb-9e80cd8ed704
Drummond, James, Foster, Jack, Gürdoğan, Ömer and Kalousios, Chrysostomos
(2021)
Tropical fans, scattering equations and amplitudes.
Journal of High Energy Physics, 2021, [71].
(doi:10.1007/JHEP11(2021)071).
Abstract
We describe a family of tropical fans related to Grassmannian cluster algebras. These fans are related to the kinematic space of massless scattering processes in a number of ways. For each fan associated to the Grassmannian Gr(k, n) there is a notion of a generalised ϕ3 amplitude and an associated set of scattering equations which further generalise the Gr(k, n) scattering equations that have been recently introduced. Here we focus mostly on the cases related to finite Grassmannian cluster algebras and we explain how face variables for the cluster polytopes are simply related to the scattering equations. For the Grassmannians Gr(4, n) the tropical fans we describe are related to the singularities (or symbol letters) of loop amplitudes in planar
= 4 super Yang-Mills theory. We show how each choice of tropical fan leads to a natural class of polylogarithms, generalising the notion of cluster adjacency and we describe how the currently known loop data fit into this classification.
Text
JHEP11(2021)071
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Accepted/In Press date: 10 November 2021
Published date: 10 November 2021
Identifiers
Local EPrints ID: 492090
URI: http://eprints.soton.ac.uk/id/eprint/492090
ISSN: 1126-6708
PURE UUID: 91157d43-b4f7-4a17-8358-44a596d702a5
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Date deposited: 16 Jul 2024 16:52
Last modified: 16 Jul 2024 16:53
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Author:
Jack Foster
Author:
Chrysostomos Kalousios
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