Abstract
We discuss the confinement properties of the CP n−1 models in more than 2 dimensions by three different approaches: by putting them on the lattice, by the 1 n expansion in 2 + ε dimensions and by semiclassical arguments based on the vortex configurations of the models. Whereas in the 1 n expansion the string-like picture of confinement holding in two dimensions turns out to be broken, we find that, both in the lattice and in the semiclassical approach a degenerate case of absolute confinement takes place, as suggested by the equivalence between CP 1 and the O(3) σ-model. It is possible to isolate the configurations which determine the degeneracy and to recognize besides them the pattern of a gauge theory with two phases, a Higgs-like and a confining one, respectively.
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