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We study properties of two-color QCD at imaginary chemical potential ($\mu$)from the viewpoint of the Roberge-Weiss (RW) periodicity, the chargeconjugation and the pseudo-reality. At $\mu=\pm i\pi T/2$, where $T$ istemperature, the system is symmetric under the combination of the chargeconjugation ${\cal C}$ and the ${\mathbb Z}_{2}$ transformation. The symmetry,called ${\cal C} {\mathbb Z}_{2}$ symmetry, is preserved at lower $T$ butbroken 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 chiralrestoration and the deconfinement are investigated by introducing theentanglement 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 isweak, but becomes first-order when the correlation is strong. We alsoinvestigate the impact of the correlation on the phase diagram at real $\mu$.

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