The construction of Atiyah, Drinfeld, Hitchin and Manin provided complete description of all instantons on Euclidean four-space. It was extended by Kronheimer and Nakajima to instantons on ALE spaces, resolutions of orbifolds |$\mathbb{R}^4/\Gamma$| by a finite subgroup Γ⊂SU(2). We consider a similar classification, in the holomorphic context, of instantons on some of the next spaces in the hierarchy, the ALF multi-Taub-NUT manifolds, showing how they tie in to the bow solutions to Nahm’s equations via the Nahm correspondence. Recently Nakajima and Takayama constructed the Coulomb branch of the moduli space of vacua of a quiver gauge theory, tying them to the same space of bow solutions. One can view our construction as describing the same manifold as the Higgs branch of the mirror gauge theory as described by Cherkis, O’Hara and Saemann. Our construction also yields the monad construction of holomorphic instanton bundles on the multi-Taub-NUT space for any classical compact Lie structure group.

中文翻译：

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古典组的瞬子和弓

Atiyah、Drinfeld、Hitchin 和 Manin 的构造提供了欧几里得四空间上所有瞬子的完整描述。它被 Kronheimer 和 Nakajima 扩展到 ALE 空间上的瞬子，orbifolds 的分辨率|$\mathbb{R}^4/\Gamma$| 由有限子群Γ⊂ SU(2). 我们考虑在全纯上下文中对层次结构中某些下一个空间的瞬时子进行类似分类，即 ALF 多 Taub-NUT 流形，显示它们如何通过 Nahm 对应关系与 Nahm 方程的弓形解相关联。最近 Nakajima 和 Takayama 构建了颤动规范理论的真空模空间的库仑分支，将它们与弓解的相同空间联系起来。人们可以将我们的构造视为描述与 Cherkis、O'Hara 和 Saemann 所描述的镜像规范理论的希格斯分支相同的流形。我们的构造还为任何经典的紧李结构群在多 Taub-NUT 空间上产生了全纯瞬子丛的单子构造。