Non-perturbative renormalization of the yang-mills beta functions

We determine the non-perturbative corrections to the gauge coupling constant and the topological charge in the Yang-Mills theory. The method makes no explicit use of instanton calculations but instead relies on boundary properties of the quantum partition function. The approach may offer important clues regarding the be-havior of the coupling constant and the theta angle for other gauge theories like QCD and supersymmetric QCD.