The ADHM Construction and Non-local Symmetries of the Self-dual Yang–Mills Equations

We construct the most general reducible connection that satisfies the self-dual Yang–Mills equations on a simply-connected, open subset of flat \mathbbR⁴{\mathbb{R}^4}. We show how all such connections lie in the orbit of the flat connection on \mathbbR⁴{\mathbb{R}^4} under the action of non-local symmetries of the self-dual Yang–Mills equations. Such connections fit naturally inside a larger class of solutions to the self-dual Yang–Mills equations that are analogous to harmonic maps of finite type.