Symbol alphabets from plabic graphs

A bstract 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 from plabic graphs by solving matrix equations of the form C ∙ Z = 0 to associate functions on Gr( m, n ) to parameterizations of certain cells of Gr( k, n ) indexed by plabic graphs. For m = 4 and n = 8 we show that this association precisely reproduces the 18 algebraic symbol letters of the two-loop NMHV eight-particle amplitude from four plabic graphs.