ZNtopology and charge confinement inSU(N)Higgs models. II

We analyze a mechanism of quark confinement by making use of a frozen Higgs model. By summing up all possible modes of topological excitations, we derive an effective Lagrangian of the model in the strong-coupling regime. These excitations are magnetic $Z_N$ vortices and magnetic $Z_N$ monopoles, which are labeled by the magnetic weight lattice and by the magnetic root lattice of $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$, respectively. The effective Lagrangian is shown to contain electric $Z_N$ vortices and electric $Z_N$ charges as topological excitations, which are labeled by the electric weight lattice and by the electric root lattice of $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$, respectively. From this fact we conclude that the $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ Higgs model gives the $N$-ality confinement of quarks in the strong-coupling regime.