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

Roberge-Weiss phase transitions and extended Z3 symmetry