Solving N=3 super-Yang-Mills equations in harmonic superspace

TL;DR

This paper develops a harmonic superspace approach to solve superfield constraints in four-dimensional N=3 super-Yang-Mills theory, simplifying equations of motion and providing an iterative solution method.

Contribution

It introduces a harmonic superspace formulation with a nilpotent gauge, enabling a simplified and iterative solution of the super-Yang-Mills equations.

Findings

Simplified superfield equations of motion using harmonic variables.

Derived a linear iterative system for solving the equations.

Provided a new gauge choice that reduces complexity.

Abstract

We analyze the superfield constraints of the D=4, N=3 SYM-theory using light-cone gauge conditions. The SU(3)/U(1)xU(1) harmonic variables are interpreted as auxiliary spectral parameters, and the transform to the harmonic-superspace representation is considered. Our nilpotent gauge for the basic harmonic superfield simplifies the SYM-equations of motion. A partial Grassmann decomposition of these equations yields the solvable linear system of iterative equations.