A noncommutative-geometric interpretation of the resolution of equivariant instanton moduli spaces

Abstract

We generalize the recently proposed noncommutative ADHM construction to the case of $\Gamma$-equivariant instantons over ${\mathbb{R}}^4$, with $\Gamma$ a Kleinian group. We show that a certain form of the inhomogeneous ADHM equations describes instantons over a noncommutative deformation of the Kleinian orbifold $\C^2/Γ$ and we discuss the relation of this with Nakajima's description of instantons over ALE spaces. In particular, we obtain a noncommutative interpretation of the minimal resolution of Kleinian singularities.

arXiv comment36 pages, no figures;small improvements of style,minor typos corrected

References in corpus (2)

• Aspects of Type IIB Theory on ALE Spaces
• Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra

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• A Note on the Hitchin System in a Background B-field