Exact regular ZN monopole solutions in gauge theories with non-adjoint Higgs representations

In this paper we give a construction of exact regular ZN monopole solutions in spontaneously broken gauge theories. These monopoles occur when a gauge group G is broken down to some multiply connected subgroup H. For finite N this can in general only be achieved by a Higgs field that does not transform under the adjoint representation of G. This implies that the usual construction of the Bogomolny equations breaks down. We show however that exact regular ZN monopoles can be constructed as solutions to the Bogomolny equations of a suitably chosen subgroup anti G. Various classes of models are analysed explicitly. (orig.)