City Research Online

Abstract

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:	Symplectic Administrator

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