Polyakov-Nambu-Jona Lasinio model and Color-Flavor-Locked phase of QCD

The effect of Polyakov loop on the QCD phase diagram at high density is studied within the Nambu-Jona Lasinio model with Polyakov loop (PNJL model). We point out that the color neutrality is missing in the standard PNJL model at finite density. Moreover, we discuss how the color-flavor locked (CFL) phase is to be distorted by the inclusion of Polyakov loop.