Infrared equivalence of strongly and weakly coupled gauge theories

Abstract

Using the decoupling theorem of Appelquist and Carazzone, we show that in terms of Feynman diagrams the pure Yang-Mills theory is equivalent in the infrared limit to a theory (zero-mass renormalized) where the vector mesons are coupled to fermions, and where the fermions do not decouple. By taking enough fermions we then show that even though the pure Yang-Mills theory is characterized by the lack of applicability of perturbation theory, nevertheless the effective coupling in the equivalent fermion description is very weak. The effective mass in the zero-mass renormalization blows up. In the fermion description, diagrams involving only vector mesons are suppressed relative to diagrams containing at least one fermion loop.