Generalized Dirac monopoles in non-Abelian Kaluza-Klein theories

A method is proposed for constructing the geometries of the non-Abelian Kaluza-Klein theories of generalized monopoles in arbitrary dimensions. These represent a natural generalization of the Euclidean Taub-NUT space, regarded as the appropriate background of the Dirac magnetic monopole. A recent theory of induced representations governing the isometries of the Euclidean Taub-NUT space is combined with usual geometrical methods obtaining a conjecture in which the potentials of the generalized monopoles can be written down without to solve explicitly the Yang-Mills equations. 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 cannot be interpreted as monopoles. The space-like models are studied pointing out that their monopole fields strength are particular solutions of the Yang-Mills equations with central symmetry, producing the standard flux of 4π through the two-dimensional spheres surrounding the monopole. Examples are given of manifolds with Einstein metrics carrying SU(2) monopoles.