Supersymmetric β Function with Ultraviolet Chop-Off

We notice that the renormalization of the effective charge in a 4-dimensional (supersymmetric) gauge theory is determined by the same graphs and is rigidly connected to the renormalization of the metric on the moduli space of the classical vacua of the corresponding reduced quantum mechanical system. Supersymmetry provides constraints for possible modifications of the metric, and this might give an alternative simple proof of nonrenormalization theorems for the original 4-dimensional theory.