*-Wars Episode I: The Phantom Anomaly

TL;DR

This paper explores the properties of chiral non-commutative gauge theories, showing they inherently cancel certain anomalies through a mechanism analogous to string theory's Green-Schwarz anomaly cancellation, highlighting UV/IR mixing effects.

Contribution

It demonstrates that non-commutative gauge theories automatically eliminate gauge and flavor anomalies via a string theory analogy, providing a new perspective on anomaly cancellation mechanisms.

Findings

All mixed gauge anomalies vanish in non-commutative theories.

ABJ flavor anomalies automatically cancel in these theories.

The anomaly cancellation is analogous to the Green-Schwarz mechanism in string theory.

Abstract

As pointed out, chiral non-commutative theories exist, and examples can be constructed via string theory. Gauge anomalies require the matter content of individual gauge group factors, including U(1) factors, to be non-chiral. All ``bad'' mixed gauge anomalies, and also all ``good'' (e.g. for $\pi ^0\to \gamma \gamma$) ABJ type flavor anomalies, automatically vanish in non-commutative gauge theories. We interpret this as being analogous to string theory, and an example of UV/IR mixing: non-commutative gauge theories automatically contain ``closed string,'' Green-Schwarz fields, which cancel these anomalies.