Nonlinear sigma model approach for chiral fluctuations and symmetry breakdown in the Nambu-Jona-Lasinio model

Tills paper is organized in two parts. We start with the observation that the recent claim that the chiral symmetry in the Nambu-Jona-Lasinio (NJL) model is necessarily restored by violent chiral fluctuations at N-c = 3 [H. Kleinert and B. Van den Bossche, Phys. Lett. B 474, 336 (2000)] appears to be incorrect since the critical stiffness of the effective nonlinear sigma model used in the above reference is not a universal quantity in 3 + 1 dimensions. In the second part we discuss a modified Nn model, where the critical stiffness is expressed via an additional cutoff parameter. This model displays a symmetry breakdown, and also under certain conditions the chiral fluctuations give rise to a phase analogous to pseudogap phase of superconductors with strong coupling or low carrier density.