Instantons on Gravitons

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35 Scopus citations


Yang-Mills instantons on ALE gravitational instantons were constructed by Kronheimer and Nakajima in terms of matrices satisfying algebraic equations. These were conveniently organized into a quiver. We construct generic Yang-Mills instantons on ALF gravitational instantons. Our data are formulated in terms of matrix-valued functions of a single variable, that are in turn organized into a bow. We introduce the general notion of a bow, its representation, its associated data and moduli space of solutions. For a judiciously chosen bow the Nahm transform maps any bow solution to an instanton on an ALF space. We demonstrate that this map respects all complex structures on the moduli spaces, so it is likely to be an isometry, and use this fact to study the asymptotics of the moduli spaces of instantons on ALF spaces.

Original languageEnglish (US)
Pages (from-to)449-483
Number of pages35
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Sep 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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