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

C. P. Martin·C. Tamarit
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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 $θ^{μν}$. We set $θ^{0i}=0$ 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 $θ^{μν}$. 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 $θ^{μν}$. We adapt our results to noncommutative gauge theories with SO(N) and U(1) gauge groups.

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C. P. Martin, C. Tamarit. 2005-05-25. The U(1)A anomaly in noncommutative SU(N) theories. https://doi.org/10.1103/physrevd.72.085008

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