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On Yang-Mills instantons over multi-centered gravitational instantons. (English) Zbl 1028.81039

Summary: In this paper we explicitly calculate the analogue of the ’t Hooft \(SU(2)\) Yang-Mills instantons on Gibbons-Hawking multi-centered gravitational instantons, which come in two parallel families: the multi-Eguchi-Hanson, or \(A_k\) ALE gravitational instantons and the multi-Taub-NUT spaces, or \(A_k\) ALF gravitational instantons. We calculate their energy and find the reducible ones. Following Kronheimer we also exploit the \(U(1)\) invariance of our solutions and study the corresponding explicit singular \(SU(2)\) magnetic monopole solutions of the Bogomolny equations on flat \(\mathbb R^3\).

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
83C57 Black holes
81V17 Gravitational interaction in quantum theory
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