ZNtopology and charge confinement inSU(N)Higgs models

We analyze topological effects in frozen $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ Higgs models in continuous space-time, where topological excitations are $Z_N$ vortices together with associated $Z_N$ monopoles. The space dimension is either two or three. We show that vortex condensation generates magnetic gauge symmetry and that monopole condensation leads to a spontaneous breakdown of this symmetry. By summing up all possible excitation modes of $Z_N$ vortices and $Z_N$ monopoles, we derive an effective Lagrangian in the strong-coupling regime. We obtain the following conclusions: (i) if external charges are introduced in the fundamental representation, they are confined by electric vortex strings, and (ii) if external charges are introduced in the adjoint representation, they are screened completely.