Confinement and ℤ₃ symmetry in three-flavor QCD

We investigate the relation between the confinement and the Z₃ symmetry in three-flavor QCD with imaginary isospin chemical potentials (μu,μd,μs) = (iT,iT, 0), using the Polyakov-loop extended NambuJonaLasinio (PNJL) model, where T is temperature. As for three-degenerate flavors, the system has ℤ₃ symmetry at = 2π/3 and hence the Polyakov loop ψ vanishes there for small T. As for 2+1 flavors, the symmetry is not preserved for any , but ψ becomes zero at = conf < 2π/3 for small T. The confinement phase defined by ψ = 0 is realized, even if the system does not have Z3 symmetry exactly. In the T plane, there is a critical endpoint of deconfinement transition. The deconfinement crossover at zero chemical potential is a remnant of the first-order deconfinement transition at = conf. The relation between the nondiagonal element X_us of quark-number susceptibilities and the deconfinement transition is studied. The present results can be checked by lattice QCD simulations directly, since the simulations are free from the sign problem for any .