String expansion as large N expansion of gauge theories Original Research Article

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 α′ → 0, the string perturbative expansion coincides with `t Hooftʹs large N expansion. We specifically concentrate on theories with d = 4 and N = 0, 1, 2, 4, and use world-sheet orbifold techniques to prove vanishing theorems for the field theory β-functions to all orders in perturbation theory in the large N limit. This is in accord with recent predictions.