N=1 and N=2 super-Yang-Mills theories from wrapped branes

We consider supergravity solutions of D5-branes wrapped on supersymmetric 2-cycles and use them to discuss relevant features of four-dimensional N = 1 and Ar = 2 super-Yang-Mills theories with gauge group SU(N). In particular in the Ar = I case, using a gravitational dual of the gaugino condensate, we obtain the complete NSVZ beta-function. We also find non-perturbative corrections associated to fractional instantons with charge 2/N. These non-perturbative effects modify the running of the coupling constant which remains finite even at small scales in a way that resembles to the soft confinement scenario of QCD. (C) 2002 Published by Elsevier Science B.V.