A Comment on Sigma Model Anomalies

Some non-linear sigma models with fermions are known to be ill-defined because of a global obstruction to any consistent quantization. Sigma models relevant to phenomenological theories of dynamical symmetry breaking must satisfy the additional constraint of appropriately realizing the flavor symmetries of the underlying theory at the one-loop level. This is possible if and only if 't Hooft's anomaly condition is satisfied. In particular, we show that there always exists a Wess-Zumino term which correctly reproduces the flavor anomalies, and the global obstruction vanishes, whenever 't Hooft's condition is satisfied.