Nonlinear sigma model approach for phase disorder transitions and the pseudogap phase in chiral Gross-Neveu, Nambu-Jona-Lasinio models and strong-coupling superconductors

TL;DR

This paper reviews the nonlinear sigma model approach to phase transitions and pseudogap phenomena in chiral models and strong-coupling superconductors, highlighting similarities with high-energy physics and recent developments.

Contribution

It systematizes recent generalizations of the nonlinear sigma model approach to particle physics, comparing pseudogap phases in superconductors with those in chiral models.

Findings

Description of two-step phase transitions in models at low N

Analysis of pseudogap phase formation in strong-coupling superconductors

Discussion of the relevance of these phenomena to QCD and color superconductors

Abstract

We briefly review the nonlinear sigma model approach for the subject of increasing interest: "two-step" phase transitions in the Gross-Neveu and the modified Nambu-Jona-Lasinio models at low $N$ and condensation from pseudogap phase in strong-coupling superconductors. Recent success in describing "Bose-type" superconductors that possess two characterstic temperatures and a pseudogap above $T_c$ is the development approximately comparable with the BCS theory. One can expect that it should have influence on high-energy physics, similar to impact of the BCS theory on this subject. Although first generalizations of this concept to particle physics were made recently, these results were not systematized. In this review we summarize this development and discuss similarities and differences of the appearence of the pseudogap phase in superconductors and the Gross-Neveu and Nambu-Jona-Lasinio - like models. We discuss its possible relevance for chiral phase transition in QCD and color superconductors. This paper is organized in three parts: in the first section we briefly review the separation of temperatures of pair formation and pair condensation in strong - coupling and low carrier density superconductors (i.e. the formation of the {\it pseudogap phase}). Second part is a review of nonlinear sigma model approach to an analogous phenomenon in the Chiral Gross-Neveu model at small N. In the third section we discuss the modified Nambu-Jona-Lasinio model where the chiral phase transition is accompanied by a formation of a phase analogous to the pseudogap phase.