Low-lying modes of the Dirac operator are expected to play an important role in spontaneous chiral symmetry breaking in QCD. We show that in the broken phase the modes at the lower edge of the spectrum are chirally polarized. The polarization vanishes as we go higher in energy and this defines a low-energy scale in QCD. As we move towards the chirally symmetric phase, either by increasing the temperature or by introducing light quark flavors in the theory, the chiral polarization scale goes down and the polarized modes disappear as the symmetry is restored. Surprisingly, the transition to the chirally restored phase passes through an intermediate phase where the Dirac operator spectrum is bimodal. In the pure-glue theory, where the deconfinement transition is sharply defined, this intermediate phase appears at the onset of deconfinement. Our conjecture is then that this intermediate phase, which seems to occur generically as we move from chirally broken to chirally restored phases, corresponds to a deconfined system with spontaneous chiral symmetry breaking.
Joint seminar of MTA-DE (Hungarian Academy of Sciences - University of Debrecen) Particle Physics Research Group and of MTA Atomki Momentum Research Group on Lattice-QCD.