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. The phase diagram of strongly interacting matter has been a subject of theoretical/experimental work since the foundation of Quantum chromodynamics (QCD). The perturbative QCD can be of some help in the extremely high density regime, but it is no longer reliable at density of physical interest. The lattice QCD is a powerfu
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