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

Abstract

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. Resent findings of a duality between the Nambu-Jona Lasinio model and the nonlinear sigma model 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 the nonlinear sigma model owing to the duality. The recent progress on interacting systems in finite systems is also reviewed.

arXiv comment24pages, 10 figures, Invited review paper commissioned by Symmetry. Comments warmly welcome

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Cited by in corpus (8)

• Casimir Force for the $\mathbb{C}{P}^{N-1}$ Model
• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Ground state modulations in the $\mathbb{C}{P}^{N-1}$ model
• Spin Statistics and Surgeries of Topological Solitons in QCD Matter in Magnetic Field
• Kink Crystalline Condensate and Multi-kink Solution in Holographic Superconductor
• Twisted kink crystal in holographic superconductor
• A domain wall and chiral edge currents in holographic chiral phase transitions