Gap in the Dirac spectrum and quark propagator symmetries in lattice QCD

TL;DR

This paper investigates the relationship between the emergence of symmetries like $SU(2)_{CS}$ in high-temperature lattice QCD and the presence of a gap in the Dirac spectrum, analyzing quark propagator invariance.

Contribution

It provides a detailed analysis of conditions under which the quark propagator remains invariant under $SU(2)_{CS}$ and related symmetries in the presence of a Dirac spectrum gap.

Findings

Identifies conditions for quark propagator invariance under $SU(2)_{CS}$.

Links the Dirac spectrum gap to symmetry emergence in high-temperature QCD.

Clarifies the role of quark propagator invariance in hadron correlators.

Abstract

Recent studies on lattice QCD have shown the emergence of large symmetries at high temperature. This includes not only the restoration $SU(n_F)_L \times SU(n_F)_R$, but also the effective emergence of an unexpected symmetry group, namely $SU(2)_{CS}$, which contains $U(1)_A$ as subgroup. At the same time, at high $T$, a gap in Dirac spectrum appears. As it is argued in several works of \textit{L. Glozman et al.}, there should be a connection between a gap in the Dirac spectrum and the presence of $SU(2)_{CS}$.In this paper, we analyze whether the quark propagator can be invariant under $SU(n_F)_L \times SU(n_F)_R$ and $SU(2)_{CS}$ transformations, in case of a gap in the Dirac spectrum, and consequently the invariance of hadron correlators, giving the condition for a quark propagator to be invariant under $SU(2)_{CS}$.