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

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 $\mu$.