How tropical are seven- and eight-particle amplitudes?
release_e4thcf4j7fhq7l3uvsnki3ngqi
by
Niklas Henke, Georgios Papathanasiou
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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