Dual condensates at finite isospin chemical potential

The dual observables as order parameters for center symmetry are tested at finite isospin chemical potential μIμI in a Polyakov-loop enhanced chiral model of QCD with physical quark masses. As a counterpart of the dressed Polyakov-loop, the first Fourier moment of pion condensate is introduced for μI>mπ/2μI>mπ/2 under the temporal twisted boundary conditions for quarks. We demonstrate that this dual condensate exhibits the similar temperature dependence as the conventional Polyakov-loop. We confirm that its rapid increase with T is driven by the evaporating of pion condensation. On the other hand, the dressed Polyakov-loop shows abnormal thermal behavior, which even decreases with T at low temperatures due to the influence of pion condensate. We also find that the dressed Polyakov-loop always rises most steeply at the chiral transition temperature, which is consistent with the previous results in Nambu–Jona-Lasinio (NJL) model and its variants without considering the center symmetry. Since both quantities are strongly affected by the chiral symmetry and pion condensation, we conclude that it is difficult to clarify the deconfinement transition from the dual condensates in this situation within this model.