Restoration of axial symmetry and its possible relation with restoration of chiral symmetry and deconfinement at finite temperature

The phase transitions characterized by deconfinement and restoration of chiral symmetry as well as the restoration of axial symmetry, at finite temperature, are investigated in the framework of SU(2) Polyakov-Nambu-Jona-Lasinio (PNJL) models with the U$_A$(1) anomaly. The thermodynamics of the phase transitions, the topological susceptibility, the meson spectrum, and, in particular, the convergence of axial and chiral partners are analyzed, in the framework of the ordinary PNJL model and in its extension, the entangled Polyakov-Nambu-Jona-Lasinio (EPNJL) model. The latter incorporates entanglement between restoration of chiral symmetry and deconfinement.