Evaluation of the Spontaneous Chiral Symmetry Breaking Scale in General Gauge Theories with Non-Perturbative Renormalization Group

We analyze the non-perturbative renormalization group in general vector-like gauge theories. The complete set of local four-fermi operators allowed by the chiral symmetry is taken into account. The beta functions for all those operators with gauge interactions are calculated. Within the four-fermi operator space, we propose two simple methods of evaluating the spontaneous chiral symmetry breaking scale. The large-N part of the system is separately evaluated and approximates the total system very well.