Polyakov loop and the color-flavor locked phase of Quantum Chromodynamics

We consider the Polyakov Nambu Jona Lasinio model with three massless quarks at high density and moderate temperature in the superconductive color flavor locking phase. We compute the critical temperature $T_c$ as a function of the baryonic chemical potential for the phase transition from the superconductive state to the normal phase. We find that $T_c$ is higher by a factor 1.5 -2 in comparison to the model containing no Polyakov loop. We also compute the specific heat $C_v$ near the second order phase transition and we show that the inclusion of the Polyakov loop does not change the value of the critical exponent.