The Bargmann symmetry constraint of the new super Dirac hierarchy

For the orthosymplectic Lie superalgebra a s p(2,2), we construct a new super Dirac integrable hierarchy, which can be written as the super Hamiltonian structure with the aid of supertrace identity. Upon choosing N distinct spectral parameters, a Bargmann symmetry constraint is proposed for the super Dirac integrable hierarchy. By substituting the symmetry constraint into N copies finite-dimensional super systems, we find the constrained super systems, defined over the supermanifold R (4N/4N), are completely integrable in the Liouville sense.