Maps for currents and anomalies in noncommutative gauge theories

We derive maps relating currents and their divergences in non-Abelian U(N) noncom-mutative gauge theory with the corresponding expressions in the ordinary (commutative) description. For the U(1) theory, in the slowly-varying-field approximation, these maps are also seen to connect the star-gauge-covariant anomaly in the noncommutative theory with the standard Adler–Bell–Jackiw anomaly in the commutative version. For arbitrary fields, derivative corrections to the maps are explicitly computed up to O(θ 2).