Nambu-Jona-Lasinio Model at the Next-to-Leading Order in 1/N

We derived and solved the compositeness condition in the Nambu-Jona-Lasinio model at the next-to-leading order in 1/N, and obtained the expressions for the effective coupling constants in terms of the compositeness scale. In the NJL model with a scalar composite, the next to leading contributions are too large for N=3. In the induced gauge theory with abelian gauge symmetry, the correction term is reasonably suppressed, while, in the SU(N_c) gauge theory with N_f flavors of fermions, the correction is suppressed only for N_f>11N_c/2, complementarily to asymptotic freedom.