On the origin of the $Nc^1$ scaling in the confined but chirally symmetric phase at high T

Abstract

There is lattice evidence that the QCD matter above the chiral restoration temperature Tch and below the deconfinement temperature Td, called stringy fluid, is characterized by an approximate chiral spin symmetry, which is a symmetry of confinement in QCD with light quarks. The energy density, pressure and entropy density in the stringy fluid scale as Nc^1, which is in contrast to the Nc^0 scaling in the hadron gas and to the Nc^2 scaling in the quark-gluon plasma. Here we clarify the origin of the Nc^1 scaling. We employ a solvable field-theoretical large $N_c$ chirally symmetric and confining model. In vacuum the confining potential induces a spontaneous breaking of chiral symmetry. The mesons are spatially localized states of quarks and antiquarks. Still in the confining regime the system undergoes the chiral restoration phase transition at $T_{ch}$ because of Paili blocking of the quark levels required for the existence of the quark condensate, by the thermal excitation of quarks and antiquarks. The same Paili blocking leads to a delocalization of the color singlet low-spin meson-like states that become infinitely large in the chiral limit. Consequently the stringy fluid represents a very dense medium of the overlapping huge color-singlet low-spin quark-antiquark systems. The Bethe-Salpeter equation that determines the rest-frame excitation energies of the color-singlet quark-antiquark system is Nc-independent both in vacuum and in the medium in the confining regime. The excitation energy of the quark-antiquark color-singlet systems scales as Nc^0, i.e. as meson mass in vacuum. The Nc^1 scaling of the energy density in the stringy fluid is provided by the fluctuations of the color-singlet quark-antiquark systems.