Non(anti)commutative Field Theories: Model Building and renormalizability properties

Abstract

We discuss one particular model of non(anti)commutative superspace. The deformation is nonhermitian and given in terms of the SUSY covariant derivatives D α. We construct a deformed Wess-Zumino action and analyze its renormalizability properties. One-loop divergences in the twopoint, three-point and four-point Green functions are calculated. In the general model we find that divergences in the four-point function cannot be absorbed and thus our model is not renormalizable. However, there is a special choice of the free parameters in the model that renders renormalizability. We discuss this choice and other possibilities to render the model renormalizable.