Duality between Chiral Symmetry Breaking and Charged Pion Condensation Phenomena in PNJL Model

This paper explores the duality between chiral symmetry breaking and charged pion condensation within the Polyakov extended Nambu–Jona-Lasinio (PNJL) model, which incorporates confinement phenomena absent in the traditional NJL model framework that describes only chiral dynamics. The PNJL model in addition incorporates the Polyakov loop to include confinement and the confinement-deconfinement transition, enabling a more comprehensive exploration of QCD phase structure under conditions of finite temperature and baryon density. The thermodynamic potential of dense quark matter with isospin and chiral imbalances obtained in PNJL model is analyzed. It is shown analytically that the duality between chiral symmetry breaking and charged pion condensation remains intact and persists in PNJL model across both confined and deconfined phases, i.e., regardless of the value of the Polyakov loop.