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 μB, isospin μI, chiral μ5, and chiral isospin μI5 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 (μB,μI,μ5,μI5)-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. Published by the American Physical Society 2025