Chiral spin states, hole dynamics, and superconductivity in strongly correlated electronic systems

Relation between strongly correlated electronic systems and anyonlike systems is established. A U(1) gauge theory is developed for the frustrated Hubbard model in the limit of infinite on-site Coulomb repulsion. An effective Chern-Simons theory, which describes chiral spin liquids is obtained. The fermions (holes) are coupled to the gauge fields creating thus an anyonlike system. I show that under some circumstances the system is a superconductor for special value of the hole density