Dual Symmetry of Effective Dense QCD Models

The properties of the symmetry of the phase diagram of dense quark matter composed of \(u\) and \(d\) three-color quarks are investigated within the framework of massless (3+1)-dimensional Nambu–Jona–Lasinio and quantum chromodynamics 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 transformation. Consequently, the full thermodynamic potentials of these models exhibit dual symmetry. This means that, on the complete \((\mu_{B},\mu_{I},\mu_{5},\mu_{I5})\) phase portraits of these models, the phases with spontaneous chiral symmetry breaking and charged pion condensation are dually conjugate (symmetric) to each other.