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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. The first paper arXiv:2007.00646 in this series focused on n=8 algebraic letters. In this paper we show that it is possible to obtain all rational symbol letters (in fact all cluster variables) by solving matrix equations of the form C Z = 0 if one allows C to be an arbitrary cluster parameterization of the top cell of Gr_+(n-4,n).
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 suggest an algorithm for computing these
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 associ
It is widely expected that NMHV amplitudes in planar, maximally supersymmetric Yang-Mills theory require symbol letters that are not rationally expressible in terms of momentum-twistor (or cluster) variables starting at two loops for eight particles.
We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of $n$-particle amplitudes in planar $mathcal{N}=4$ Yang-Mills theory and certain polytopes associated to the Grassmannian G(4,
Planar bicolored (plabic) graphs are combinatorial objects introduced by Postnikov to give parameterizations of the positroid cells of the totally nonnegative Grassmannian $text{Gr}^{geq 0}(n,k)$. Any two plabic graphs for the same positroid cell can