Dual meson condensates in the Polyakov-loop extended linear sigma model

Dual meson condensates as possible order parameters for deconfinement are investigated in a Polyakov-loop enhanced linear sigma model of QCD at both zero and finite isospin chemical potential ${\mu }_I$. We find that the rapid rise of the dual sigma condensate (corresponding to the dressed Polyakov-loop) with $T$ is driven by the chiral transition, no matter whether the Polyakov-loop dynamics is included or not. For ${\mu }_I>m_{\pi }\mathrm{/}2$, the dual sigma condensate shows abnormal thermal behavior which even decreases with $T$ below the melting temperature $T_c^{I_3}$ of pion superfluidity; On the other hand, even the dual pion condensate always increases with $T$, its maximum slope locates exactly at $T_c^{I_3}$ rather than the deconfinement temperature $T_c^P$ determined by the Polyakov-loop. All these are qualitatively consistent with the previous results obtained in the Nambu-Jona-Lasinio type models. The dual vector meson condensate for ${\mu }_I>m_{\pi }\mathrm{/}2$ is also calculated. This quantity is more sensitive to the chiral transition when taking into account the Dirac-sea contribution. Our study further suggests that it should be cautious to use dual observables to indicate the deconfinement transition, especially in QCD models.