On the Anomalies and Schwinger Terms in Noncommutative Gauge Theories

TL;DR

This paper reexamines the invariant anomaly in noncommutative QED, revealing the necessity of both UV and IR regularizations to properly identify anomalies and deriving related Schwinger terms.

Contribution

It demonstrates the need for IR regularization alongside UV in noncommutative gauge theories to correctly identify invariant anomalies and provides explicit expressions and Schwinger terms.

Findings

Both UV and IR regularizations are essential for anomaly detection.

An explicit expression for the invariant anomaly is derived.

Schwinger terms of the current algebra are calculated.

Abstract

Invariant (nonplanar) anomaly of noncommutative QED is reexamined. It is found that just as in ordinary gauge theory UV regularization is needed to discover anomalies, in noncommutative case, in addition, an IR regularization is also required to exhibit existence of invariant anomaly. Thus resolving the controversy in the value of invariant anomaly, an expression for the unintergrated anomaly is found. Schwinger terms of the current algebra of the theory are derived.