# On the origin of the Nc1 scaling in the confined but chirally symmetric phase at high T

## TL;DR

The paper explains why a specific scaling pattern in high-temperature QCD matter arises, linking it to the behavior of quark-antiquark systems.

## Contribution

The paper clarifies the origin of the Nc^1 scaling in the confined, chirally symmetric phase of QCD.

## Key findings

- The Nc^1 scaling in the stringy fluid is due to fluctuations of color-singlet quark-antiquark systems.
- Chiral restoration at Tch is caused by Pauli blocking from thermal quark-antiquark excitation.
- The Bethe–Salpeter equation for quark-antiquark systems is Nc-independent in the confining regime.

## Abstract

There is lattice evidence that the QCD matter above the chiral restoration temperature \documentclass[12pt]{minimal}
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\begin{document}$$T_{ch}$$\end{document}Tch and below the deconfinement temperature \documentclass[12pt]{minimal}
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\begin{document}$$T_d$$\end{document}Td, called stringy fluid, is characterized by 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 \documentclass[12pt]{minimal}
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\begin{document}$$N_c^1$$\end{document}Nc1, which is in contrast to the \documentclass[12pt]{minimal}
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\begin{document}$$N_c^0$$\end{document}Nc0 scaling in the hadron gas and to the \documentclass[12pt]{minimal}
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\begin{document}$$N_c^2$$\end{document}Nc2 scaling in the quark-gluon plasma. Here we clarify the origin of the \documentclass[12pt]{minimal}
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\begin{document}$$N_c^1$$\end{document}Nc1 scaling. We employ a solvable field-theoretical large \documentclass[12pt]{minimal}
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\begin{document}$$N_c$$\end{document}Nc 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 \documentclass[12pt]{minimal}
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\begin{document}$$T_{ch}$$\end{document}Tch 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 \documentclass[12pt]{minimal}
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\begin{document}$$N_c$$\end{document}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 \documentclass[12pt]{minimal}
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\begin{document}$$N_c^0$$\end{document}Nc0, i.e. as meson mass in vacuum. The \documentclass[12pt]{minimal}
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\begin{document}$$N_c^1$$\end{document}Nc1 scaling of the energy density in the stringy fluid is provided by the fluctuations of the color-singlet quark-antiquark systems.