Gauged Wess–Zumino model in noncommutative Minkowski superspace

Abstract

We develop a gauged Wess–Zumino model in noncommutative Minkowski superspace. This is the natural extension of the work of Carlson and Nazaryan, which extended N=1∕2 supersymmetry written over deformed Euclidean superspace to Minkowski superspace. We investigate the coupling of the vector and chiral superfields. Noncommutativity is implemented by replacing products with star products. Although, in general, our star product is nonassociative, we prove that it is associative to the first order in the deformation parameter C. We show that our model reproduces the N=1∕2 theory in the appropriate limit, namely when the deformation parameters C¯α̇β̇=0. Essentially, we find the N=1∕2 theory and a conjugate copy. As in the N=1∕2 theory, a reparametrization of the gauge parameter, vector superfield, and chiral superfield are necessary to write standard C-independent gauge theory. However, our choice of parametrization differs from that used in the N=1∕2 supersymmetry, which leads to some unexpected new terms.