Superconductivity in strongly correlated electronic systems and confinement versus deconfinement phenomenon

The supersymmetrical gauge theory of strongly correlated electronic systems, based on a geometrical approach to the quantization of the Hubbard model, is presented. It is shown that topological magnetic excitations induce the long-distance interaction between the charged particles. This interaction, depending on the statistics of the magnetic excitations, leads to the confinement or statistical transmutation phenomenon and finally to the superconductivity. The long-wave theory of the short-range-order antiferromagnetic insulator state is proposed.