Integrability of N = 3 super Yang-Mills equations

TL;DR

This paper presents a harmonic superspace formulation of N=3 super Yang-Mills equations, transforming them into holomorphicity conditions that simplify the construction of solutions and deepen understanding of their integrability.

Contribution

It introduces a novel harmonic superspace approach to recast N=3 super Yang-Mills equations as holomorphicity conditions, facilitating solution construction.

Findings

Reformulation of equations as Cauchy-Riemann-like conditions

Simplified explicit solution construction

Enhanced understanding of integrability properties

Abstract

We describe the harmonic superspace formulation of the Witten-Manin supertwistor correspondence for N=3 extended super Yang-Mills theories. The essence is that on being sufficiently supersymmetrised (up to the N=3 extension), the Yang-Mills equations of motion can be recast in the form of Cauchy-Riemann-like holomorphicity conditions for a pair of prepotentials in the appropriate harmonic superspace. This formulation makes the explicit construction of solutions a rather more tractable proposition than previous attempts.