AdS$_{5}$ factor. By requiring that the effective action in field theory has an exact $SL(2,Z)$ symmetry, we are able to fix the form of the six derivative terms. After performing a field redefinition on the field theory side ,,, the form of the field theory effective action and probe action agree up to and including six derivative contributions. This computation is a simple extension of the result reported in  for the ${\cal N}=4$ case. The new feature is the identification of the explicit $N$ dependence of the background coupling which is needed to exhibit the expected overall $N$ dependence of the probe action.

The next example we study is the theory with $N_{f}=4$ massive flavors. The presence of the flavor masses explicitly breaks the conformal invariance. Indeed, the coupling of this theory picks up a dependence on the energy scale of the theory due to instanton corrections. Solutions of this type are particularly interesting from the point of view of the gravity/field theory connection. The radial direction of the AdS$_{5}$ space plays the role of an energy scale in the conformal field theory case. However, all beta functions in the conformal field theory vanish and the evolution under the renormalization 