Surviving on the Slope: Supersymmetric Vacuum in the Theories Where It Is Not Supposed to Be

In supersymmetric models with the run-away vacua or with the stable but non-supersymmetric ground state there exist stable field configurations (vacua) which restore one half of supersymmetry and are characterized by constant positive energy density. The formal foundation for such vacua is provided by the central extension of the N =1 superalgebra with the infinite central charge.