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

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

2005-04-20

arxiv.org/abs/hep-th/0504171v1

Phys.Lett. B620 (2005) 187-194

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, no figures

Scientific paper

10.1016/j.physletb.2005.06.028

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.

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