Renormalization of the Topological Charge in Yang-Mills Theory

TL;DR

This paper investigates how quantum effects in four-dimensional Yang-Mills theory lead to the renormalization of the topological charge and theta parameter, with implications for the strong CP problem in QCD.

Contribution

It demonstrates that gauge bosons cause a finite multiplicative renormalization of the theta parameter, and fermions induce an additional shift, using a truncated renormalization group approach.

Findings

Gauge bosons cause finite multiplicative renormalization of theta.

Fermions induce an additional shift in theta.

Implications for the strong CP problem are discussed.

Abstract

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 theta--parameter while fermions give rise to an additional shift of theta. A truncated form of an exact renormalization group equation is used to study the scale dependence of the theta--parameter. Possible implications for the strong CP--problem of QCD are discussed.