  The linear $SU(2)_L \times SU(2)_R$ sigma-model occupies a unique place in
elementary particle physics and quantum field theory. It has been recently
realized that when a chemical potential for hypercharge is added, it becomes a
toy model for the description of the dynamics of the kaon condensate in high
density QCD. We review recent results in nonperturbative dynamics obtained in
the ungauged and gauged versions of this model.
