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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. Supersymmetric Seiberg–Witten map for noncommutative superspace is employed to obtain an action in terms of commuting fields at the first order in the noncommutativity parameter θ. This leads to a gauge invariant theory for U(1) gauge group whose θ deformed supersymmetry transformations are presented. Non–abelian case is also discussed.