Infrared equivalence of strongly and weakly coupled gauge theories

Using the decoupling theorem of Appelquist and Carazzone, it is shown 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 it is then shown 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. (Auth.)