Two-Dimensional Integrable Systems and Self-Dual Yang-Mills Equations

TL;DR

This paper explores the connection between 2D integrable systems and 4D self-dual Yang-Mills equations, providing a method to relate these through twistor theory and zero-curvature representations, with explicit examples of special self-dual connections.

Contribution

It introduces a novel method to associate self-dual Yang-Mills connections with integrable systems like KdV and nonlinear Schrödinger equations using twistor and zero-curvature frameworks.

Findings

Constructed explicit self-dual connections without two independent conformal symmetries.

Established a systematic association between integrable systems and self-dual Yang-Mills equations.

Demonstrated the use of twistor description in linking 2D integrable models to 4D gauge theories.

Abstract

The relation between two--dimensional integrable systems and four--dimen\-sional self--dual Yang--Mills equations is considered. Within the twistor description and the zero--curvature representation a method is given to associate self--dual Yang-Mills connections with integrable systems of the Korteweg--de Vries and non--linear Schr\"odinger type or principal chiral models. Examples of self--dual connections are constructed that as points in the moduli do not have two independent conformal symmetries.