Confined but chirally and chiral spin symmetric hot matter
We investigate properties of the quark--antiquark mesons at zero and finite temperature in the framework of a solvable chirally symmetric quark model with linear confining potential. The interquark interaction in the model is reminiscent of that derived in Coulomb gauge QCD, with the string tension being the only model parameter. We demonstrate that while the confining interaction induces spontaneous breaking of chiral symmetry at T=0, chiral symmetry gets restored at a temperature Tch ~ 90 MeV for the string tension fixed to provide the phenomenological value of the quark condensate. This temperature is similar to Tch ~ 130 MeV observed on the lattice in the chiral limit for N_c=3. The physical mechanism responsible for the chiral symmetry restoration in the confining regime is Pauli blocking of the quark levels, required for the existence of a nonvanishing quark condensate, by the thermal excitations of the quarks and antiquarks. Thus, above the chiral restoration temperature, the meson-like states are chirally symmetric and approximately chiral spin symmetric. A crucial property of the confined meson-like light-light states above Tch is their size that exceeds drastically that in the chirally broken phase below Tch, in contrast to the heavy-heavy mesons that nearly preserve their size irrespective of the temperature. This property is a result of Pauli blocking of the quark and antiquark levels with small momenta. Furthermore, the root-mean-square radius of the states with J=0,1 diverges in the chiral limit. This unexpected property must be a key to understanding unusual features of the hot QCD matter as observed at RHIC and LHC. Consequently, the confining but chirally symmetric matter above Tch can be considered as a dense system of very large and strongly overlapping meson-like states (``strings'').