City Research Online

Abstract

We study tropical Grassmanians Tr(k, n) in relation to cluster algebras, and assess their applicability to n-particle amplitudes for n = 7, 8. In N = 4 super Yang-Mills theory, we first show that while the totally positive part of Tr(4, 7) may encompass the iterated discontinuity structure of the seven-point Maximally Helicity Violating (MHV) amplitude, it is too small for the Next-to-MHV helicity configuration. Then, using Tr(4, 8) we propose a finite set of 356 cluster A-coordinates expected to contain the rational symbol letters of the eight-particle MHV amplitude, and discuss how the remaining square-root letters may be obtained from limits of infinite mutation sequences. Finally, we use a triangulation of the totally positive part of Tr(3, 8) to obtain the associated generalised biadjoint scalar amplitude in a form containing a near-minimal amount of spurious poles.

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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