Z22-graded supersymmetry via superfield on minimalZ22-superspace

Abstract

A superfield formalism for the minimal Z2 2-graded version of supersymmetry is developed. This is done by using the recently introduced definition of integration on the minimal Z2 2-superspace. It is shown that one may construct Z2 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 Z2 2-graded extension of many known theories defined in two-dimensional spacetime. 
As an illustration, we will give a Z2 2-extension of the sine-Gordon model different from the one already discussed in the literature.