The quarkynic phase and the Z_{Nc} symmetry

We investigate the interplay between the Z_{Nc} symmetry and the emergence of the quarkyonic phase, adding the flavor-dependent complex chemical potentials \mu_f=\mu+iT\theta_f with (\theta_f)=(0, \theta, -\theta) to the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model. When \theta=0, the PNJL model with the \mu_f agrees with the standard PNJL model with the real chemical potential \mu. When \theta=2\pi/3, meanwhile, the PNJL model with the \mu_f has the Z_{Nc} symmetry exactly for any real \mu, so that the quarkyonic phase exists at small T and large \mu. Once \theta varies from 2\pi/3, the quarkyonic phase exists only on a line of T=0 and \mu larger than the dynamical quark mass, and the region at small T and large \mu is dominated by the quarkyonic-like phase in which the Polyakov loop is small but finite.