Dulaity and charged pion condensation in chirally asymmetric dense quark matter in the framework of an NJL$_2$ model

TL;DR

This paper explores the phase structure of a (1+1)-dimensional quark model with chemical potentials, revealing a duality between chiral symmetry breaking and pion condensation, and showing that chiral isospin chemical potential induces charged pion condensation with baryon density.

Contribution

It demonstrates the duality between chiral symmetry breaking and pion condensation phases and shows that chiral isospin chemical potential induces charged pion condensation with baryon density in the model.

Findings

Duality between chiral symmetry breaking and pion condensation phases.

Chiral isospin chemical potential induces charged pion condensation with baryon density.

Inhomogeneous charged pion condensate phase appears at small chiral isospin chemical potential.

Abstract

In this talk we present investigation of the phase structure of a (1+1)-dimensional quark model with four-quark interaction and in the presence of baryon ($\mu_B$), isospin ($\mu_I$) and chiral isospin ($\mu_{I5}$) chemical potentials. Spatially homogeneous and inhomogeneous (chiral density wave (for chiral condensate) and single wave (for charged pion condensate)) condensates are considered. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation one. The primary conclusion of this investigation is the fact that chiral isospin chemical potential generates charged pion condensation with non-zero baryon density in dense quark matter. Moreover, it is shown that inhomogeneous charged PC phase with nonzero baryon density is induced in the model by arbitrary small values of the chemical potential $\mu_{I5}$ (for a rather large region of $\mu_B$ and $\mu_I$).