Dualities in dense quark matter with isospin, chiral and chiral isospin imbalance in the framework of the large-N$_{c}$ limit of the NJL$_{4}$ model

TL;DR

This paper explores the phase structure of dense quark matter under various chemical potentials using the large-Nc limit of the NJL4 model, revealing dualities and conditions for pion condensation.

Contribution

It uncovers three duality correspondences in the NJL4 model and demonstrates how chiral and chiral isospin chemical potentials influence phase transitions.

Findings

Existence of three dualities in the model.

Chiral isospin chemical potential can induce pion condensation.

Chiral chemical potential alone can also generate pion condensation at low densities.

Abstract

In this paper the phase structure of the dense quark matter has been investigated in the presence of baryon ${\mu}_B$, isospin ${\mu}_I$, chiral ${\mu}_{5}$ and chiral isospin ${\mu}_{I5}$ chemical potentials in the framework of Nambu--Jona-Lasinio model. It has been shown that in the large-$N_{c}$ limit ($N_{c}$ is the number of quark colours) there exist three duality correspondences in the model. The first duality is between the chiral symmetry breaking and the charged pion condensation phenomena. And there are two new dualities that hold only for chiral symmetry breaking and charged pion condensation phenomena separately. It was shown that at nonzero chiral ${\mu}_{5}$ chemical potential chiral isospin ${\mu}_{I5}$ chemical potential can generate charged pion condensation in dense quark matter even with zero ${\mu}_{I}$. But ${\mu}_{5}$ alone (in absence of ${\mu}_{I5}$ chemical potential) can generate this phase but not as powerfully as ${\mu}_{I5}$ does and only at comparatively low baryon densities.