Harmonic-Superspace Method Of Solving N=3 Super-Yang-Mills Equations

TL;DR

This paper introduces a harmonic-superspace approach to solving N=3 super-Yang-Mills equations, simplifying the superfield constraints and transforming them into a finite set of linear equations.

Contribution

It develops a harmonic-superspace method that simplifies N=3 SYM equations using light-cone gauge and nilpotent harmonic superfield equations.

Findings

Harmonic superfield equations are equivalent to finite linear iterative equations.

Harmonic transform matrices and gauge connections become nilpotent on-shell.

The method simplifies solving N=3 SYM equations significantly.

Abstract

We analyze the superfield constraints of the D=4, N=3 SYM-theory using light-cone gauge conditions. The SU(3)/U(1) x U(1) harmonic variables are interpreted as auxiliary spectral parameters, and the transform to the harmonic-superspace representation is considered. The harmonic superfield equations of motion are drastically simplified in our gauge, in particular, the basic matrix of the harmonic transform and the corresponding harmonic analytic gauge connections become nilpotent on-shell. It is shown that these harmonic SYM-equations are equivalent to the finite set of solvable linear iterative equations.