Tropical fans, scattering equations and amplitudes
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 ϕ 3 amplitude and an as...
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2021
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oai:doaj.org-article:0ccce1702d8e4417901f772659d7aa582021-11-14T12:40:30ZTropical fans, scattering equations and amplitudes10.1007/JHEP11(2021)0711029-8479https://doaj.org/article/0ccce1702d8e4417901f772659d7aa582021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)071https://doaj.org/toc/1029-8479Abstract 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 ϕ 3 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 N $$ \mathcal{N} $$ = 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.James DrummondJack FosterÖmer GürdoğanChrysostomos KalousiosSpringerOpenarticleDifferential and Algebraic GeometryScattering AmplitudesNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-27 (2021) |
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DOAJ |
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DOAJ |
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EN |
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Differential and Algebraic Geometry Scattering Amplitudes Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 |
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Differential and Algebraic Geometry Scattering Amplitudes Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 James Drummond Jack Foster Ömer Gürdoğan Chrysostomos Kalousios Tropical fans, scattering equations and amplitudes |
| description |
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 ϕ 3 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 N $$ \mathcal{N} $$ = 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. |
| format |
article |
| author |
James Drummond Jack Foster Ömer Gürdoğan Chrysostomos Kalousios |
| author_facet |
James Drummond Jack Foster Ömer Gürdoğan Chrysostomos Kalousios |
| author_sort |
James Drummond |
| title |
Tropical fans, scattering equations and amplitudes |
| title_short |
Tropical fans, scattering equations and amplitudes |
| title_full |
Tropical fans, scattering equations and amplitudes |
| title_fullStr |
Tropical fans, scattering equations and amplitudes |
| title_full_unstemmed |
Tropical fans, scattering equations and amplitudes |
| title_sort |
tropical fans, scattering equations and amplitudes |
| publisher |
SpringerOpen |
| publishDate |
2021 |
| url |
https://doaj.org/article/0ccce1702d8e4417901f772659d7aa58 |
| work_keys_str_mv |
AT jamesdrummond tropicalfansscatteringequationsandamplitudes AT jackfoster tropicalfansscatteringequationsandamplitudes AT omergurdogan tropicalfansscatteringequationsandamplitudes AT chrysostomoskalousios tropicalfansscatteringequationsandamplitudes |
| _version_ |
1718429089119862784 |