Renormalization of the topological charge in Yang-Mills theory

The conditions leading to a nontrivial renormalization of the topological charge in four-dimensional Yang-Mills theory are discussed. It is shown that if the topological term is regarded as the limit of a certain nontopological interaction, quantum effects due to the gauge bosons lead to a finite multiplicative renormalization of the θ-parameter while fermions give rise to an additional shift of θ. A truncated form of an exact renormalization group equation is used to study the scale dependence of the θ-parameter. Possible implications for the strong CP-problem of QCD are discussed. (orig.)