Noncommutative SU(N) theories, the axial anomaly, Fujikawa's method and the Atiyah-Singer index

Abstract

Fujikawa's method is employed to compute at first order in the noncommutative parameter the $U(1{)}_A$ anomaly for noncommutative SU(N). We consider the most general Seiberg-Witten map which commutes with hermiticity and complex conjugation and a noncommutative matrix parameter, ${\theta }^{\mu \nu }$, which is of ``magnetic'' type. Our results for SU(N) can be readily generalized to cover the case of general nonsemisimple gauge groups when the symmetric Seiberg-Witten map is used. Connection with the Atiyah-Singer index theorem is also made.

11 pages, no figures

References in corpus (1)

• The U(1)A anomaly in noncommutative SU(N) theories

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