  We consider string perturbative expansion in the presence of D-branes
imbedded in orbifolded space-time. In the regime where the string coupling is
weak and $\alpha'\to 0$, the string perturbative expansion coincides with `t
Hooft's large N expansion. We specifically concentrate on theories with d=4 and
${\cal N}=0,1,2,4$, and use world-sheet orbifold techniques to prove vanishing
theorems for the field theory beta functions to all orders in perturbation
theory in the large N limit. This is in accord with recent predictions.
