Chemical potentials and parity breaking: the Nambu-Jona-Lasinio model

Abstract

We consider the "two flavour" Nambu--Jona-Lasinio model in the presence of a vector and an axial external chemical potentials and study the phase structure of the model at zero temperature. The Nambu--Jona-Lasinio model is often used as a toy replica of QCD and it is therefore interesting to explore the consequences of adding external vector and axial chemical potentials in this model, mostly motivated by claims that such external drivers could trigger a phase where parity could be broken in QCD. We are also motivated by some lattice analysis that attempt to understand the nature of the so-called Aoki phase using this simplified model. Analogies and differences with the expected behaviour in QCD are discussed and the limitations of the model are pointed out.

16 pages, 13 figures

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• Phase structure of a generalized Nambu Jona-Lasinio model with Wilson fermions in the mean field or large $N$-expansion

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• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Dense baryon matter with isospin and chiral imbalance in the framework of NJL${}_4$ model at large $N_c$: duality between chiral symmetry breaking and charged pion condensation
• Spontaneous chiral symmetry breaking and the Chiral Magnetic Effect for interacting Dirac fermions with chiral imbalance
• Charged pion condensation and duality in dense and hot chirally and isospin asymmetric quark matter in the framework of NJL${}_2$ model
• Competition and duality correspondence between chiral and superconducting channels in (2+1)-dimensional four-fermion models with fermion number and chiral chemical potentials
• Duality between chiral symmetry breaking and charged pion condensation at large $N_c$: Consideration of an NJL${}_2$ model with baryon-, isospin- and chiral isospin chemical potentials
• Charged pion condensation in dense quark matter: Nambu--Jona-Lasinio model study
• Catalysis of Dynamical Chiral Symmetry Breaking by Chiral Chemical Potential in Dirac semimetals
• Competition and duality correspondence between inhomogeneous fermion-antifermion and fermion-fermion condensations in the NJL${}_2$ model
• Analysis of dilepton angular distributions in a parity breaking medium
• Interplay between superconductivity and chiral symmetry breaking in a (2+1)-dimensional model with compactified spatial coordinate
• Chiral perturbation theory for nonzero chiral imbalance
• Chiral symmetry breaking with no bilinear condensate revisited
• QCD phase diagram with chiral imbalance in NJL model: duality and lattice QCD results
• Kondo effect driven by chirality imbalance
• Effect of chiral imbalance on the electrical conductivity of hot and dense quark matter using Green-Kubo Method within the 2-flavour gauged NJL model
• Shear and bulk viscous coefficients of a hot and chirally imbalanced quark matter using NJL model
• Dense Baryonic Matter and Applications of QCD Phase Diagram Dualities
• Searching for P- and CP-odd effects in heavy ion collisions