Renormalization in the Gauged Nambu-Jona-Lasinio Model

Based on the Cornwall-Jackiw-Tomboulis effective potential, we extensivelystudy nonperturbative renormalization of the gauged Nambu-Jona-Lasinio model inthe ladder approximation with standing gauge coupling. Although the pureNambu-Jona-Lasinio model is not renormalizable, presence of the gaugeinteraction makes it possible that the theory is renormalized as an interactingcontinuum theory at the critical line in the ladder approximation. Extra higherdimensional operators (``counter terms'') are not needed for the theory to berenormalized. By virtue of the effective potential approach, therenormalization (``symmetric renormalization'') is performed in aphase-independent manner both for the symmetric and the spontaneously brokenphases of the chiral symmetry. We explicitly obtain $\beta$ function having anontrivial ultraviolet fixed line for the renormalized coupling as well as thebare one. In both phases the anomalous dimension is very large ($ \ge 1$)without discontinuity across the fixed line. Operator product expansion isexplicitly constructed, which is consistent with the large anomalous dimensionowing to the appearance of the nontrivial extra power behavior in the Wilsoncoefficient for the unit operator. The symmetric renormalization breaks down atthe critical gauge coupling, which is cured by the generalized renormalizationscheme (``$\tM$-dependent renormalization''). Also emphasized is the formalresemblance to the four-fermion theory in less than four dimensions which isrenormalizable in $1/N$ expansion.Comment: 72 pages, 12 figures (not included), LaTeX file, KEK-TH-344/KEK preprint 92-86/CHIBA-EP-65/DPNU-92-2