Symbol Alphabets from Plabic Graphs II: Rational Letters

TL;DR

This paper demonstrates a method to derive all rational symbol letters for n-particle amplitudes in N=4 super-Yang-Mills theory by solving specific matrix equations related to cluster variables.

Contribution

It introduces a novel approach to obtain all rational symbol letters using matrix equations and cluster parameterizations of the Grassmannian's top cell.

Findings

All rational symbol letters can be derived from matrix equations C Z = 0.

The method connects cluster variables with matrix parameterizations of Gr_+(n-4,n).

Provides a systematic way to generate symbol alphabets for scattering amplitudes.

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. 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).