Anomalies in noncommutative gauge theories, Seiberg-Witten transformation and Ramond-Ramond couplings

We propose an exact expression for the unintegrated form of the star gauge-invariant axial anomaly in an arbitrary even dimensional noncommutative gauge theory. The proposal is based on our earlier work,7 as well as on the inverse Seiberg-Witten map and identities related to it, obtained previously(15,18) by comparing Ramond-Ramond couplings in different descriptions. The integrated anomalies, found from the unintegrated ones, are expressed in terms of a simplified version of the Elliott formula involving the noncommutative Chern character. These anomalies, under the Seiberg-Witten transformation, reduce to the ordinary (integrated) axial anomalies. Compatibility with existing results of anomalies in noncommutative theories is established.