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Gauge anomalies and the Witten-Seiberg correspondence for N=1 supersymmetric theories on noncommutative spaces

The explicit form of non-Abelian noncommutative supersymmetric (SUSY) chiral anomaly is calculated, the Wess-Zumino consistency condition is verified and the correspondence of the Yang-Mills sector to the previously obtained results is shown. We generalize the Seiberg-Witten map to the case of N=1 SUSY Yang-Mills theory and calculations up to the second order in the noncommutativity parameter are done.