Generalized Dirac monopoles in non-Abelian Kaluza-Klein theories

TL;DR

This paper develops a method to generalize Dirac monopoles to non-Abelian Kaluza-Klein theories, introducing new time-like monopole models and analyzing their properties within Einstein manifolds.

Contribution

It proposes a unified geometric approach to define generalized monopole potentials in higher dimensions using principal fiber bundles, including novel time-like monopole models.

Findings

Space-like monopole models solve Yang-Mills equations with flux $4\,\pi$.

Existence of new time-like monopole models beyond standard interpretations.

Examples include Einstein manifolds with SU(2) monopoles.

Abstract

A method is proposed for generalizing the Euclidean Taub-NUT space, regarded as the appropriate background of the Dirac magnetic monopole, to non-Abelian Kaluza-Klein theories involving potentials of generalized monopoles. Usual geometrical methods combined with a recent theory of the induced representations governing the Taub-NUT isometries lead to a general conjecture where the potentials of the generalized monopoles of any dimensions can be defined in the base manifolds of suitable principal fiber bundles. Moreover, in this way one finds that apart from the monopole models which are of a space-like type, there exists a new type of time-like models that can not be interpreted as monopoles. The space-like models are studied pointing out that the monopole fields strength are particular solutions the Yang-Mills equations with central symmetry producing the standard flux of $4\pi$ through the two-dimensional spheres surrounding the monopole. Examples are given of manifolds with Einstein metrics carrying SU(2) monopoles.