Comments of Z22-supersymmetry in superfield formalism

Abstract

We investigate superfield formulation of the minimal Z22-supersymmetry. It is shown that the integrability on Z22-superspace guarantees the invariance of action. Then we present two superfields which carry distinct irreducible representations of the Z22-supersymmetry algebra. One of them gives integrable Lagrangian and the other does not. We also show that integrable superfields with different Z22-degree also carry irreducible representations and they give invariant actions. To perform this analysis, the representation theory of the minimal Z22-supersymmetry algebra is studied in some detail.