How tropical are seven- and eight-particle amplitudes?
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:
-
Journal of High Energy Physics
- Pub Date:
- August 2020
- DOI:
- 10.1007/JHEP08(2020)005
- arXiv:
- arXiv:1912.08254
- Bibcode:
- 2020JHEP...08..005H
- Keywords:
-
- 1/N Expansion;
- Extended Supersymmetry;
- Scattering Amplitudes;
- Supersymmetric Gauge Theory;
- High Energy Physics - Theory
- E-Print:
- 47 pages, 7 tables, 14 figures, 2 ancillary files