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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 μ_f=μ+iTθ_f with (θ_f)=(0, θ, -θ) to the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model. When θ=0, the PNJL model with the μ_f agrees with the standard PNJL model with the real chemical potential μ. When θ=2π/3, meanwhile, the PNJL model with the μ_f has the Z_{Nc} symmetry exactly for any real μ, so that the quarkyonic phase exists at small T and large μ. Once θvaries from 2π/3, the quarkyonic phase exists only on a line of T=0 and μlarger than the dynamical quark mass, and the region at small T and large μis dominated by the quarkyonic-like phase in which the Polyakov loop is small but finite.