The covariant form of the gauge anomaly on noncommutative R2n

TL;DR

This paper derives the covariant gauge anomaly for non-Abelian gauge theories on noncommutative R2n, analyzing its properties, origin, and relation to the consistent anomaly, with implications for bi-fundamental matter.

Contribution

It provides the explicit form of the covariant gauge anomaly on noncommutative R2n and explores its connection to the consistent anomaly, including the anomaly-free nature of bi-fundamental matter.

Findings

Covariant gauge anomaly computed for U(N) on noncommutative R2n.

Connection established between covariant and consistent anomalies.

Bi-fundamental matter has no mixed anomalies due to half-dipole structure.

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.