Consequences of the non-abelian anomaly in supersymmetric theories

In supersymmetric theories, the anomalous interactions involving the Goldstone supermultiplets are found not to be determined from supersymmetry considerations alone: they depend also on the dynamical details of the model. The origin of the unexpected results lies in the presence of the massless fermionic superpartners of the Goldstone bosons. For example, the decay $\pi^0 \rightarrow \gamma \gamma $ is found to be suppressed in supersymmetric QCD (SQCD). Low-energy effective actions with the correct symmetry properties are constructed, taking SQCD as an illustrative example. The axion decay $a \rightarrow \gamma \gamma$ in a supersymmetric composite model might be suppressed with the same mechanism that works for $\pi^0 \rightarrow \gamma \gamma $ in SQCD.