Dual symmetries of dense three and two-color QCD and some QCD-like NJL models

Abstract

In this paper the symmetry properties of the phase diagram of dense quark matter composed of $u$ and $d$ quarks with two or three colors has been investigated in the framework of massless (3+1)-dimensional Nambu--Jona-Lasinio (NJL) and QCD models. It turns out that in the presence of baryon $\mu_B$, isospin $\mu_I$, chiral $\mu_5$ and chiral isospin $\mu_{I5}$ chemical potentials the Lagrangians of these models are invariant under the so-called dual transformations. Consequently, the entire NJL model (or QCD) thermodynamic potentials are dually symmetric. In particular, it means that in the total $(\mu_B,\mu_I,\mu_5,\mu_{I5})$-phase portraits of these models the chiral symmetry breaking (CSB) and charged pion condensation (PC) phases are arranged dually conjugated (or symmetrical) to each other (in the case of three-color models). Whereas in the case of two-color quark matter, these models predict the entire phase structure in which there are dual symmetries between CSB, charged PC and baryon superfluid phases.