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We propose an exact expression for the unintegrated form of the star gaugeinvariant axial anomaly in an arbitrary even dimensional gauge theory. Theproposal is based on the inverse Seiberg-Witten map and identities related toit, obtained earlier by comparing Ramond-Ramond couplings in differentdecsriptions. The integrated anomalies are expressed in terms of a simplifiedversion of the Elliott formula involving the noncommutative Chern character.These anomalies, under the Seiberg-Witten transformation, reduce to theordinary axial anomalies. Compatibility with existing results of anomalies innoncommutative theories is established.Comment: 16 pages. LaTe

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