Roberge-Weiss phase transitions and extended Z3 symmetry

TL;DR

This paper investigates the connection between Roberge-Weiss phase transitions and extended Z3 symmetry using the PNJL model with imaginary chemical potential, revealing symmetry breaking causes phase transition discontinuities.

Contribution

It demonstrates how the transition from continuous to discrete symmetry in the PNJL model explains the RW phase transition behavior.

Findings

At low temperature, approximate continuous symmetry allows smooth Polyakov loop oscillations.

At high temperature, symmetry breaks to extended Z3, causing Polyakov loop discontinuities.

The symmetry breaking explains the RW phase transition mechanism.

Abstract

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.