Instantons on Gravitons
arXiv:1007.0044 · doi:10.1007/s00220-011-1293-y
Abstract
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.
42 pages, 8 figures
References in corpus (5)
- Moduli Spaces of Instantons on the Taub-NUT Space
- Quiver Varieties and Branching
- A hyperkahler structure on the cotangent bundle of a complex Lie group
- Framed Rank r Torsion-free Sheaves on CP^2 and Representations of the Affine Lie Algebra \hat{gl(r)}
- On some asymptotically flat manifolds with non maximal volume growth