Confinement/Deconfinement Transition of Large N Gauge Theories in Perturbation Theory with N_f Fundamentals: N_f/N Finite

In hep-th/0402219 we considered large N zero-coupling d-dimensional U(N) gauge theories, with N_f matter fields in the fundamental representation on a compact spatial manifold S^{d-1}x time, with N_f/N finite. This class of theories undergo a 3rd order deconfinement transition. As a consequence it was proposed that the dual string theory has a 3rd order phase-transition to a black hole at high temperature. In this paper we argue that the same conclusions are valid for such theories at any finite order in perturbation theory in the 't Hooft coupling lambda and N_f/N. It is conjectured that this continues to hold at strong coupling and finite value of N_f/N < (1/lambda), which suggests that the supergravity approximation to the dual string theory has a 3rd order thermal phase transition to a large black hole.