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

TL;DR

This study explores the phase structure of dense quark matter under various chemical potentials using the NJL model, revealing a duality between chiral symmetry breaking and pion condensation, with chiral isospin potential inducing pion condensation.

Contribution

It demonstrates a duality between chiral symmetry breaking and pion condensation in dense quark matter within the NJL model at large N_c, highlighting the role of chiral isospin chemical potential.

Findings

Duality between chiral symmetry breaking and pion condensation.

Chiral isospin chemical potential induces pion condensation.

Charged pion condensation occurs in dense quark matter with isospin asymmetry.

Abstract

In this paper the phase structure of dense quark matter has been investigated in the presence of baryon, isospin and chiral isospin chemical potentials in the framework of (3+1)-dimensional Nambu--Jona-Lasinio model with two quark flavors. It has been shown that in the large-$N_{c}$ limit ($N_{c}$ is the number of colors of quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation one. The key conclusion of our studies is the fact that chiral isospin chemical potential generates charged pion condensation in dense quark matter with isotopic asymmetry.