  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.
