Instantons and Bows for the Classical Groups

Sergey A. Cherkis, Jacques Hurtubise

Research output: Contribution to journalArticlepeer-review

Abstract

The construction of Atiyah, Drinfeld, Hitchin, and Manin [AHDM78] 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 R4{Γ by a finite subgroup Γ Ă SUp2q. 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.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Jul 8 2020

ASJC Scopus subject areas

  • General

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