How tropical are seven- and eight-particle amplitudes? release_e4thcf4j7fhq7l3uvsnki3ngqi

by Niklas Henke, Georgios Papathanasiou

Released as a article .

2019  

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.
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Type  article
Stage   submitted
Date   2019-12-17
Version   v1
Language   en ?
arXiv  1912.08254v1
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