Z² ₂-graded supersymmetry via superfield on minimal Z² ₂-superspace

A superfield formalism for the minimal Z 2 2 -graded version of supersymmetry is developed. This is done by using the recently introduced definition of integration on the minimal Z 2 2 -superspace. It is shown that one may construct Z 2 2 -supersymmetric action by the procedure similar to the standard supersymmetry. However, the Lagrangian obtained has very general interaction terms, which give rise to a Z 2 2 -graded extension of many known theories defined in two-dimensional spacetime. As an illustration, we will give a Z 2 2 -extension of the sine-Gordon model different from the one already discussed in the literature.