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Chiral Phase Transition for SU(N) Gauge Theories

We describe the chiral phase transition for vector-like SU(N) gauge theories as a function of the number of quark flavors Nf by making use of an anomaly-induced effective potential. The potential depends explicitly on the full beta-function and the anomalous dimension γof the quark mass operator. By using this potential we argue that chiral symmetry is restored for γ<1. A perturbative computation of γthen leads to an estimate of the critical value Nf^c for the transition.