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

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.