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A QCD-like theory with the ZNc symmetry

We propose a QCD-like theory with the ZNc symmetry. The flavor-dependent twisted boundary condition (TBC) is imposed on Nc degenerate flavor quarksin the SU(Nc) gauge theory. The QCD-like theory is useful to understand the mechanism of color confinement. Dynamics of the QCD-like theory is studied by imposing the TBC on the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model. The TBC model is applied to two- and three-color cases. The ZNc symmetry is preserved below some temperature Tc, but spontaneously broken above Tc. The color confinement below Tc preserves the flavor symmetry. Above Tc, the flavor symmetry is broken, but the breaking is suppressed by the entanglement between the Polyakov loop and the chiral condensate. Particularly at low temperature, dynamics of the TBC model is similar to that of the PNJL model with the standard fermion boundary condition, indicating that the ZNc symmetry is a good approximate concept in the latter model even if the current quark mass is small. The present prediction can be tested in future by lattice QCD, since the QCD-like theory has no sign problem.