Polyakov loop extended NJL 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 ${mathbb Z}_{3}$ symmetry that QCD does. Quantities invariant under the extended ${mathbb Z}_{3}$ symmetry, such as the partition function, the chiral condensate and the modified Polyakov loop, have the Roberge-Weiss (RW) periodicity. The phase diagram of confinement/deconfinement transition derived with the PNJL model is consistent with the RW prediction on it and the results of lattice QCD. The phase diagram of chiral transition is also presented by the PNJL model.