  There exists a class of gauge models incorporating a finite density of matter
in which the Higgs mechanism is provided by condensates of gauge (or gauge and
scalar) fields, i.e., there are vector condensates in this case. We describe
vortex solutions in the simplest model in this class, the gauged $SU(2)\times
U(1)_Y$ $\sigma$-model with the chemical potential for hypercharge $Y$, in
which the gauge symmetry is completely broken. It is shown that there are three
types of topologically stable vortices in the model, connected either with
photon field or hypercharge gauge field, or with both of them. Explicit vortex
solutions are numerically found and their energy per unit length are
calculated. The relevance of these solutions for the gluonic phase in the dense
two-flavor QCD is discussed.
