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Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry

Henke, N. ORCID: 0000-0001-9867-2005 & Papathanasiou, G. ORCID: 0000-0002-2627-9906 (2021). Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry. Journal of High Energy Physics, 2021(10), article number 7. doi: 10.1007/jhep10(2021)007


We further exploit the relation between tropical Grassmannians and Gr(4, n) cluster algebras in order to make and refine predictions for the singularities of scattering amplitudes in planar
N = 4 super Yang-Mills theory at higher multiplicity n ≥ 8. As a mathematical foundation that provides access to square-root symbol letters in principle for any n, we analyse infinite mutation sequences in cluster algebras with general coefficients. First specialising our analysis to the eight-particle amplitude, and comparing it with a recent, closely related approach based on scattering diagrams, we find that the only additional letters the latter provides are the two square roots associated to the four-mass box. In combination with a tropical rule for selecting a finite subset of variables of the infinite Gr(4, 9) cluster algebra, we then apply our results to obtain a collection of 3, 078 rational and 2, 349 square-root letters expected to appear in the nine-particle amplitude. In particular these contain the alphabet found in an explicit 2-loop NMHV symbol calculation at this multiplicity.

Publication Type: Article
Additional Information: This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Publisher Keywords: 1/N Expansion, Extended Supersymmetry, Scattering Amplitudes, Supersymmetric Gauge Theory
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Science & Technology
School of Science & Technology > Mathematics
SWORD Depositor:
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