Symbol Alphabets from Plabic Graphs

Understand

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-point amplitude from four plabic graphs.