Nonplanar Anomalies in Noncommutative Theories and the Green-Schwarz Mechanism

TL;DR

This paper investigates nonplanar anomalies in noncommutative gauge theories, showing their conditions, implications for axial charge conservation, and how the Green-Schwarz mechanism can cancel certain anomalies, with specific examples involving D3 branes.

Contribution

It demonstrates the existence of nonplanar anomalies at zero noncommutative momentum and explores anomaly cancellation via the Green-Schwarz mechanism in noncommutative theories.

Findings

Nonplanar anomalies occur at zero noncommutative momentum.

Green-Schwarz mechanism can cancel nonplanar local anomalies.

Global anomalies, like pi0 decay, remain uncanceled.

Abstract

We discuss nonplanar anomalies in noncommutative gauge theories. In particular we show that a nonplanar anomaly exists when the external noncommutative momentum is zero and that it leads to a non-conservation of the associated axial charge. In the case of nonplanar local anomalies, a cancellation of the anomaly can be achieved by a Green-Schwarz mechanism. In an example of D3 branes placed on orbifold singularity that leads to a chiral theory, the mechanism involves twisted RR fields which propagate with zero noncommutative momentum. Global anomalies are not cancelled and, in particular, the decay pi0 --> 2 gamma is allowed.