ANOMALIES IN NONCOMMUTATIVE GAUGE THEORIES, SEIBERG–WITTEN TRANSFORMATION AND RAMOND–RAMOND COUPLINGS

Abstract

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 previously15,18 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.