  Using the Polyakov extended Nambu-Jona-Lasinio (PNJL) model with imaginary
chemical potential, the relation between the Roberge-Weiss (RW) phase
transition and the extended Z3 symmetry is studied. At low temperature, there
is approximate continuous symmetry under the phase transformation of the
Polyakov loop with the shift of the imaginary chemical potential. Due to this
continuous symmetry, the Polyakov loop can oscillate smoothly as the imaginary
chemical potential increases. At high temperature, this continuous symmetry is
broken to an exact discrete symmetry, the extended Z3 symmetry, and the
Polyakov loop can not oscillate smoothly. This symmetry breaking of the
continuous symmetry causes a discontinuity of the Polyakov loop. That is the RW
phase transition.
