  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.

High Energy Physics - Phenomenology;High Energy Physics - Lattice;High Energy Physics - Theory;Nuclear Theory