  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.
