论文标题
古典群
Instantons and Bows for the Classical Groups
论文作者
论文摘要
Atiyah，Drinfeld，Hitchin和Manin [ADHM78]的构建提供了欧几里得四空间上所有Instantons的完整描述。它是由Kronheimer和Nakajima扩展到在啤酒空间上插入的。歧管，表明它们如何通过NAHM通信与Nahm的方程式[CHE09]绑定到弓解决方案。最近，基于[Nak03]的[Nak18a]和[NT17]，Nakajima和Takayama建造了Quiver仪表理论真空的Moduli空间的库仑分支，将它们绑在了弓形解决方案的相同空间上。人们可以将我们的构造视为描述与镜面理论[COS11]的希格斯分支相同的歧管。我们的构造还产生了单态插入式捆绑的单块构造，用于任何经典的紧凑型谎言结构组。
The construction of Atiyah, Drinfeld, Hitchin, and Manin [ADHM78] 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 $\mathbb{R}^4/Γ$ by a finite subgroup $Γ\subset SU(2).$ 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 [Che09] via the Nahm correspondence. Recently in [Nak18a] and [NT17], based on [Nak03], 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 [COS11]. Our construction also yields the monad construction of holomorphic instanton bundles on the multi-Taub-NUT space for any classical compact Lie structure group.
