Nonplanar Anomalies in Noncommutative Theories and the Green-Schwarz Mechanism

We discuss nonplanar anomalies in noncommutative gauge theories. In particular we show that a nonplanar anomaly exists when the external noncommutative momentum is zero and that it leads to a non-conservation of the associated axial charge. In the case of nonplanar local anomalies, a cancellation of the anomaly can be achieved by a Green-Schwarz mechanism. In an example of D3 branes placed on orbifold singularity that leads to a chiral theory, the mechanism involves twisted RR field which propagates with zero noncommutative momentum. Global anomalies are not cancelled and, in particular, the decay pi0 --> 2 gamma is allowed.