Reducible connections and non-local symmetries of the self-dual Yang-Mills equations

Details Reducible connections and non-local symmetries of the self-dual Yang-Mills equations Reducible connections and non-local symmetries of the self-dual Yang-Mills equations

2008-12-11

arxiv.org/abs/0812.2147v2

Commun.Math.Phys.296:429-446,2010

Physics

Mathematical Physics

AMSLatex, 15 pages, no figures. Corrected in line with the referee's comments. In particular, restriction to simply-connected

Scientific paper

10.1007/s00220-010-1025-8

We construct the most general reducible connection that satisfies the self-dual Yang-Mills equations on a simply connected, open subset of flat $\mathbb{R}^4$. We show how all such connections lie in the orbit of the flat connection on $\mathbb{R}^4$ 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.

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