Two-color QCD at imaginary chemical potential and its impact on real chemical potential

TL;DR

This paper explores the properties of two-color QCD at imaginary chemical potential, examining symmetry behaviors and phase transitions, and investigates how these findings influence the phase diagram at real chemical potential.

Contribution

It introduces a detailed analysis of ${ m C} { m Z}_2$ symmetry and its breaking in two-color QCD at imaginary chemical potential, and studies the impact of chiral-deconfinement correlation on phase transitions and the phase diagram.

Findings

${ m C} { m Z}_2$ symmetry is preserved at low T and broken at high T.

The order of symmetry breaking at the RW endpoint depends on the correlation strength.

The phase diagram at real chemical potential is affected by the correlation between chiral restoration and deconfinement.

Abstract

We study properties of two-color QCD at imaginary chemical potential ($\mu$) from the viewpoint of the Roberge-Weiss (RW) periodicity, the charge conjugation and the pseudo-reality. At $\mu=\pm i\pi T/2$, where $T$ is temperature, the system is symmetric under the combination of the charge conjugation ${\cal C}$ and the ${\mathbb Z}_{2}$ transformation. The symmetry, called ${\cal C} {\mathbb Z}_{2}$ symmetry, is preserved at lower $T$ but broken at higher $T$. The Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model has the same properties as two-color QCD for ${\cal C} {\mathbb Z}_{2}$ symmetry and the pseudo-reality. The nontrivial correlation between the chiral restoration and the deconfinement are investigated by introducing the entanglement vertex in the PNJL model. The order of ${\cal C} {\mathbb Z}_{2}$ symmetry breaking at the RW endpoint is second-order when the correlation is weak, but becomes first-order when the correlation is strong. We also investigate the impact of the correlation on the phase diagram at real $\mu$.