Phase diagram in the imaginary chemical potential region and extended Z3 symmetry

Phase transitions in the imaginary chemical potential region are studied by the Polyakov-loop extended Nambu-Jona-Lasinio model that possesses the extended Z3 symmetry. The extended-Z3 invariant quantities such as the partition function, the chiral condensate, and the modified Polyakov loop have the Roberge-Weiss (RW) periodicity. There appear four types of phase transitions: deconfinement, chiral, Polyakov-loop RW, and chiral RW transitions. The orders of the chiral and deconfinement transitions depend on the presence or absence of current quark mass, but those of the Polyakov-loop RW and chiral RW transitions do not. The scalar-type, eight-quark interaction newly added in the model makes the chiral transition line shift to the vicinity of the deconfinement transition line.