Abstract
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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Communicated by N.A. Nekrasov
To David E. Williams
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Grant, J.D.E. Reducible Connections and Non-local Symmetries of the Self-dual Yang–Mills Equations. Commun. Math. Phys. 296, 429–446 (2010). https://doi.org/10.1007/s00220-010-1025-8
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DOI: https://doi.org/10.1007/s00220-010-1025-8