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

Abstract

We work out the one-loop $U(1{)}_A$ anomaly for noncommutative SU(N) gauge theories up to second order in the noncommutative parameter ${\theta }^{\mu \nu }$. We set ${\theta }^{0i}=0$ and conclude that there is no breaking of the classical $U(1{)}_A$ symmetry of the theory coming from the contributions that are either linear or quadratic in ${\theta }^{\mu \nu }$. Of course, the ordinary anomalous contributions will be still with us. We also show that the one-loop conservation of the nonsinglet currents holds at least up to second order in ${\theta }^{\mu \nu }$. We adapt our results to noncommutative gauge theories with SO(N) and U(1) gauge groups.

arXiv comment50 pages, 5 figures in eps files. Some comments and references added

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• Remarks on the 2nd order Seiberg-Witten maps
• Noncommutative QCD, first-order-in-theta-deformed instantons and 't Hooft vertices
• Noncommutative SU(N) theories, the axial anomaly, Fujikawa's method and the Atiyah-Singer index
• Adler-Bell-Jackiw anomaly in VSR electrodynamics
• Path integral analysis of the axial anomaly in Very Special Relativity