Discrete chiral symmetry breaking in QCD and Gribov unambigous potentials

Classification of vaccum states in QCD based on the nontrivial homotopic group π1 is treated. The earlier studied Gribov vacuum states fall under this classification. These states are discussed in connection with the discrete chiral symmetry breaking and with solution of the Θ-period puzzle. Similar phenomena are considered making use of well-understood models. There are the SUSY gluodynamics and the two-dimensional U(1) gauge model with Nf quarks, where Nf - flavor numbers of a theory