Symbol Alphabets from Plabic Graphs

TL;DR

This paper introduces an algorithm to compute symbol alphabets of scattering amplitudes in N=4 super-Yang-Mills theory using plabic graphs, successfully reproducing known algebraic symbol letters for specific cases.

Contribution

The paper presents a novel algorithm linking plabic graphs to symbol alphabets, enabling computation of algebraic functions in scattering amplitudes.

Findings

Reproduces 18 algebraic symbol letters for two-loop NMHV eight-point amplitude.

Establishes a method to derive symbol alphabets from plabic graphs.

Connects cluster variables and algebraic functions in amplitude computations.

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 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.