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

TL;DR

This paper calculates the one-loop U(1)_A anomaly in noncommutative SU(N) gauge theories up to second order in the noncommutative parameter, finding no new symmetry breaking contributions at this order.

Contribution

It provides the first detailed analysis of the U(1)_A anomaly in noncommutative SU(N) theories up to second order in theta, showing no additional anomaly contributions.

Findings

No breaking of U(1)_A symmetry up to second order in theta.

Conservation of nonsinglet currents holds at least up to second order.

Results extend to SO(N) and U(1) gauge groups.

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.