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

C. P. Martin·C. Tamarit
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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, $θ^{μν}$, 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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C. P. Martin, C. Tamarit. 2005-04-20. Noncommutative SU(N) theories, the axial anomaly, Fujikawa's method and the Atiyah-Singer index. https://doi.org/10.1016/j.physletb.2005.06.028

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