Instantons on Gravitons |
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Authors: | Sergey A Cherkis |
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Institution: | 1.School of Mathematics and Hamilton Mathematics Institute,Trinity College Dublin,Dublin 2,Ireland;2.Center for Theoretical Physics, Department of Physics,University of California,Berkeley,USA;3.Department of Mathematics,Stanford University,Stanford,USA |
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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. |
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