The ADHM construction and non-local symmetries of the self-dual Yang-Mills equations

TL;DR

This paper explores how non-local symmetries act on instanton moduli spaces in self-dual Yang-Mills equations, using the ADHM construction to identify symmetry subgroups and their geometric effects.

Contribution

It demonstrates that a sub-algebra of non-local symmetries generates the tangent space to the instanton moduli space and identifies the subgroup preserving the one-instanton moduli space.

Findings

A sub-algebra of the symmetry algebra generates the tangent space to the moduli space.

The subgroup preserving the one-instanton moduli space corresponds to scaling.

Explicit description of symmetry actions on instanton moduli spaces.

Abstract

We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang-Mills equations on $\mathbb{R}^4$ discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the symmetry algebra generates the tangent space to the instanton moduli space at each point. We explicitly find the subgroup of the symmetry group that preserves the one-instanton moduli space. This action simply corresponds to a scaling of the moduli space.