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.
Cite
@article{arxiv.1710.00764,
title = {Yang-Mills instantons in Kaehler spaces with one holomorphic isometry},
author = {Samuele Chimento and Tomas Ortin and Alejandro Ruiperez},
journal= {arXiv preprint arXiv:1710.00764},
year = {2018}
}
Comments
Latex2e file, 16 pages, no figures