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.

Close

PrevNext

View figure in article