YangMills instantons in Kähler spaces with one holomorphic isometry
Abstract
We consider selfdual YangMills instantons in 4dimensional Kähler spaces with one holomorphic isometry and show that they satisfy a generalization of the Bogomol'nyi equation for magnetic monopoles on certain 3dimensional metrics. We then search for solutions of this equation in 3dimensional metrics foliated by 2dimensional 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 equations 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 Kähler space. We work out completely a few explicit examples for some Kähler spaces of interest.
 Publication:

Physics Letters B
 Pub Date:
 March 2018
 DOI:
 10.1016/j.physletb.2018.01.046
 arXiv:
 arXiv:1710.00764
 Bibcode:
 2018PhLB..778..371C
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 Latex2e file, 16 pages, no figures