Symbol Alphabets from Plabic Graphs III: n=9

Authors:
  • JMJorge Mago
    Jorge Mago
  • ASAnders Schreiber
    Anders Schreiber
  • MSMarcus Spradlin
    Marcus Spradlin
  • ASAkshay Yelleshpur Srikant
    Akshay Yelleshpur Srikant
  • AVAnastasia Volovich
    Anastasia Volovich
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Abstract
Symbol alphabets of n-particle amplitudes in N=4 super-Yang-Mills theory are known to contain certain cluster variables of Gr(4,n) as well as certain algebraic functions of cluster variables. In this paper we solve the C Z = 0 matrix equations associated to several cells of the totally non-negative Grassmannian, combining methods of arXiv:2012.15812 for rational letters and arXiv:2007.00646 for algebraic letters. We identify sets of parameterizations of the top cell of Gr_+(5,9) for which the solutions produce all of (and only) the cluster variable letters of the 2-loop nine-particle NMHV amplitude, and identify plabic graphs from which all of its algebraic letters originate.