*-Wars episode I: the phantom anomaly Original Research Article

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 π0→γγ) 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.