The covariant form of the gauge anomaly on noncommutative R2n

Abstract

The covariant form of the non-Abelian gauge anomaly on noncommutative R2n is computed for U(N) groups. Its origin and properties are analyzed. Its connection with the consistent form of the gauge anomaly is established. We show along the way that bi-fundamental $U(N)\times U(M)$ chiral matter carries no mixed anomalies, and interpret this result as a consequence of the half-dipole structure which characterizes the charged non-commutative degrees of freedom.