Gauged Wess-Zumino Model in Noncommutative Minkowski Superspace

TL;DR

This paper extends the gauged Wess-Zumino model to noncommutative Minkowski superspace, exploring the effects of noncommutativity on supersymmetric gauge theories and demonstrating the model's consistency with known N=1/2 theories.

Contribution

It introduces a new formulation of the gauged Wess-Zumino model in noncommutative Minkowski superspace, including a novel associative star product to first order and a different parameterization from previous N=1/2 models.

Findings

Star product is associative to first order in deformation parameter.

Model reproduces N=1/2 supersymmetry in the appropriate limit.

New terms arise due to different parameterization choices.

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 interaction 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. We show that our model reproduces the N=1/2 theory in the appropriate limit. Essentially, we find the N=1/2 theory and a conjugate copy. As in the N=1/2 theory, a reparameterization of the gauge parameter, vector superfield and chiral superfield are necessary to write standard C-independent gauge theory. However, our choice of parameterization differs from that used in the N=1/2 supersymmetry, which leads to some unexpected new terms.