Short-distance symmetries, the axial anomaly, and the conformal group

We discuss symmetry at small distances, focusing in particular on the implementation of the conformal group. In the framework of a theory which generates strong interactions from a non-Abelian gauge group, we show that the existence of the axial anomaly—which determines the amplitude for ${\pi }^0\to 2\gamma$—as well as the nonrenormalization theorem for this anomaly may be regarded as consequences of conformal symmetry.