Noncommutative SU(N) theories, the axial anomaly, Fujikawa's method and   the Atiyah-Singer index
  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. 
C.P. Martin (Universidad Complutense de Madrid) and C. Tamarit   (Universidad Complutense de Madrid)