# Symmetries of spatial meson correlators in high temperature QCD

## TL;DR

This study identifies an intermediate temperature regime in high-temperature QCD where chiral symmetry is restored, yet correlators suggest emergent symmetries and bound quark states, indicating a complex transition from confined to free quark behavior.

## Contribution

It reveals the emergence of $SU(2)_{CS}$ and $SU(4)$ symmetries in spatial correlators at intermediate temperatures, not present in free quark models.

## Key findings

- Chiral symmetry is restored between 220-500 MeV.
- Emergent $SU(2)_{CS}$ and $SU(4)$ symmetries are observed in this regime.
- Transition to free quark behavior occurs above 1 GeV.

## Abstract

Based on a complete set of $J = 0$ and $J=1$ spatial isovector correlation functions calculated with $N_F = 2$ domain wall fermions we identify an intermediate temperature regime of $T \sim 220 - 500$ MeV ($1.2T_c$--$2.8T_c$), where chiral symmetry is restored but the correlators are not yet compatible with a simple free quark behavior. More specifically, in the temperature range $T \sim 220 - 500$ MeV we identify a multiplet structure of spatial correlators that suggests emergent $SU(2)_{CS}$ and $SU(4)$ symmetries, which are not symmetries of the free Dirac action. The symmetry breaking effects in this temperature range are less than 5%. Our results indicate that at these temperatures the chromo-magnetic interaction is suppressed and the elementary degrees of freedom are chirally symmetric quarks bound into color-singlet objects by the chromo-electric component of the gluon field. At temperatures between 500 and 660 MeV the emergent $SU(2)_{CS}$ and $SU(4)$ symmetries disappear and one observes a smooth transition to the regime above $T \sim 1$ GeV where only chiral symmetries survive, which are finally compatible with quasi-free quarks.