Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems

We review various connections between condensed matter systems with the Nambu–Jona-Lasinio model and nonlinear sigma models. The field theoretical description of interacting systems offers a systematic framework to describe the dynamical generation of condensates. Recent findings of a duality between the Nambu–Jona-Lasinio model and nonlinear sigma models enables us to investigate various properties underlying both theories. In this review, we mainly focus on inhomogeneous condensations in static situations. The various methods developed in the Nambu–Jona-Lasinio model reveal the inhomogeneous phase structures and also yield new inhomogeneous solutions in nonlinear sigma models owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.