N ≤ 1/2 supersymmetric gauge theory in noncommutative space

A formulation of (non-anticommutative) N ≤ 1/2 supersymmetric U(N) gauge theory in noncommutative space is studied. We show that at one loop UV/IR mixing occurs. A generalization of Seiberg-Witten map to noncommutative and non-anticommutative superspace is employed to obtain an action in terms of commuting fields at first order in the noncommutativity parameter . This leads to Abelian and non-Abelian gauge theories whose supersymmetry transformations are local and non-local, respectively.