We study the Renormalization Group (RG) flow of critical bosonic background fields in the framework of the RG approach to string theory. In this approach quantum field theory beta -functions are the extra inputs in solving the string theory sigma-model equations. We study two different situations, the first one is the Yang-Mills theory where the coupling constant diverges in the infrared limit. The second case corresponds to a type of theories where the beta -function has a pole in the infrared limit and it changes sign through the pole (as in N = 1 super-Yang-Mills theory). For this case in the strong coupling branch, in the infrared, there is an interval of values of the coupling in which the theory only leads to confinement. We have obtained this range. We also mention the theories with conformal-fixed points and their relation to theories with a pole in the beta -functions. We calculate the Wilson loops in these theories. (C) 2000 Elsevier Science B.V. All rights reserved.