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-colour 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 µB, isospin µI, chiral µ5, and chiral isospin µI5 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 (µB, µI, µ5 , µI5) phase portraits of these models, the phases with spontaneous chiral symmetry breaking and charged pion condensation are dually conjugate (symmetric) to each other.