We study the chiral phase transition for vector-like SU(N) gauge theories as a function of the number of quark flavors N_f by making use of an anomaly-induced effective potential. We modify an effective potential of a previous work, suggested for N_f < N, and apply it to larger values of N_f where the phase transition is expected to occur. The new effective potential depends explicitly on the full \beta-function and the anomalous dimension \gamma of the quark mass operator. By using this potential we argue that chiral symmetry is restored for \gamma <1. A perturbative computation of \gamma then leads to an estimate of the critical value N_f^c for the transition.
Schechter, Joseph and Sannino, Francesco, "Chiral Phase Transition for SU(N) Gauge Theories via an Effective Lagrangian Approach" (1990). Physics. 294.
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