Anomaly and Nonplanar Diagrams in Noncommutative Gauge Theories

Anomalies in relation to nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomaly for noncommutative U(1) and U(N) gauge theories with adjoint matter fields is determined perturbatively and shown to vanish for both planar and nonplanar diagrams. For U(1) gauge theory with fundamental matter field coupling, three different noncommutative currents are found, which give the same global symmetry and lead to the same classically conserved charge. Only one of these currents yields a nonplanar contribution and leads to a finite global anomaly for light-like noncommutativity parameter θμν , of a novel form.