Polyakov loop extended Nambu–Jona-Lasinio model with imaginary chemical potential

The Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model with imaginary chemical potential is studied. The model possesses the extended Z₃ symmetry that QCD does. Quantities invariant under the extended Z₃ symmetry, such as the partition function, the chiral condensate, and the modified Polyakov loop, have Roberge-Weiss periodicity. The phase diagram of confinement/deconfinement transition derived with the PNJL model is consistent with the Roberge-Weiss prediction on it and the results of lattice QCD. The phase diagram of chiral transition is also presented by the PNJL model.