*-Wars Episode I: The Phantom Anomaly

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.