Planar and Nonplanar Konishi Anomalies and Effective Superpotential for Noncommutative N=1 Supersymmetric U(1)
arXiv:hep-th/0307155 · doi:10.1142/S0217751X05021312
Abstract
The Konishi anomalies for noncommutative N=1 supersymmetric U(1) gauge theory arising 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 effective superpotential of the theory. In the limit of vanishing |Θp|, with Θthe noncommutativity parameter, the noncommutative effective superpotential depends on a gauge invariant superfield, which includes supersymmetric Wilson lines, and has nontrivial dependence on the gauge field supermultiplet.
arXiv commentLaTeX, 36 pages. Version 2: Typos Corrected. Version 3: Extensively revised version, 42 pages, to be published in Int. J. Mod. Phys. A. (2005)
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