Yang-Mills instantons in Kaehler spaces with one holomorphic isometry

Abstract

We consider self-dual Yang-Mills instantons in 4-dimensional Kaehler spaces with one holomorphic isometry and show that they satisfy a generalization of the Bogomol'nyi equation for magnetic monopoles on certain 3-dimensional metrics. We then search for solutions of this equation in 3-dimensional metrics foliated by 2-dimensional spheres, hyperboloids or planes in the case in which the gauge group coincides with the isometry group of the metric (SO(3), SO(1,2) and ISO(2), respectively). Using a generalized hedgehog ansatz the Bogomol'nyi quations reduce to a simple differential equation in the radial variable which admits a universal solution and, in some cases, a particular one, from which one finally recovers instanton solutions in the original Kaehler space. We work out completely a few explicit examples for some Kaehler spaces of interest.

Latex2e file, 16 pages, no figures

References in corpus (8)

• Characterization of all the supersymmetric solutions of gauged N=1,d=5 supergravity
• Resolution of SU(2) monopole singularities by oxidation
• Dyonic black holes at arbitrary locations
• Non-Abelian bubbles in microstate geometries
• A gravitating Yang-Mills instanton
• A non-Abelian Black Ring
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Cited by in corpus (2)

• Supersymmetric solutions of the cosmological, gauged, C magic model
• Non-Abelian Rotating Black Holes in 4- and 5-Dimensional Gauged Supergravity