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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Henke, N., Papathanasiou, G. How tropical are seven- and eight-particle amplitudes?. J. High Energ. Phys. 2020, 5 (2020). https://doi.org/10.1007/JHEP08(2020)005
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DOI: https://doi.org/10.1007/JHEP08(2020)005