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arXiv · 1912.08254

How tropical are seven- and eight-particle amplitudes?

Niklas Henke·Georgios Papathanasiou
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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 $\mathcal{N}=4$ 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 $\mathcal{A}$-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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Niklas Henke, Georgios Papathanasiou. 2019-12-17. How tropical are seven- and eight-particle amplitudes?. https://doi.org/10.1007/jhep08(2020)005

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