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

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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.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, 1090, Wien, Austria

    James D. E. Grant

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  1. James D. E. Grant
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Correspondence to James D. E. Grant.

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Communicated by N.A. Nekrasov

To Nicola Ramsay

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Grant, J.D.E. The ADHM Construction and Non-local Symmetries of the Self-dual Yang–Mills Equations. Commun. Math. Phys. 296, 405–428 (2010). https://doi.org/10.1007/s00220-010-1024-9

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