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The Konishi anomalies for noncommutative N=1 supersymmetric U(1) gauge theory arsing from planar and nonplanar diagrams are calculated. Whereas planar Konishi anomaly is the expected $\star$-deformation of the commutative anomaly, nonplanar anomaly reflects the important features of nonplanar diagrams of noncommutative gauge theories, such as UV/IR mixing and the appearance of nonlocal open Wilson lines. We use the planar and nonplanar Konishi anomalies to calculate the Wilsonian low energy effective superpotential in the limit of large and small noncommutativity parameter, and find its dependence on a gauge invariant superfield ${\cal{S}}$ which includes supersymmetric Wilson line, and has nontrivial dependence on the gauge supermultiplet.
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