Axial Anomaly in Noncommutative QED on R^4

The axial anomaly of the noncommutative U(1) gauge theory is calculated by a number of methods and compared with the commutative one. It is found to be given by the corresponding Chern class.Comment: LaTeX, axodraw.sty; v2: typos are fixed; v3: version to appear in Int. J. Mod. Phys. A. (2001

Anomaly and Nonplanar Diagrams in Noncommutative Gauge Theories

Anomalies arising from nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomalies for both noncommutative U(1) and U(N) gauge theories with adjoint matter fields are shown to vanish. For noncommutative QED with fundamental matters, due to UV/IR mixing a finite anomaly emerges from the nonplanar contributions. It involves a generalized $\star$-product of gauge fields.Comment: 28 pages, Latex, axodraw.sty; v2: version to appear in Int. J. Mod. Phys. A. (2001

Planar and Nonplanar Konishi Anomalies and Effective Superpotential for Noncommutative N=1 Supersymmetric U(1)

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 |\Theta p|, with \Theta the 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.Comment: LaTeX, 36 pages. Version 2: Typos Corrected. Version 3: Extensively revised version, 42 pages, to be published in Int. J. Mod. Phys. A. (2005