Non-trivial Center Dominance in High Temperature QCD

TL;DR

This paper studies the properties of quarks and gluons above the chiral transition temperature in high-temperature QCD, revealing a dominant non-trivial $Z(3)$ center structure and its effects on quark propagators, supported by lattice simulations and perturbation theory.

Contribution

It demonstrates the dominance of $Z(3)$ center twisted configurations in high-temperature QCD and connects this behavior to the renormalization group analysis, providing new insights into the thermal ensemble structure.

Findings

Thermal ensemble dominated by $Z(3)$ twisted configurations at high T.

Quark propagator at extremely high T matches free quark behavior with $Z(3)$ twisted boundary conditions.

Transition from $Z(3)$ twisted to trivial configurations occurs as quark mass exceeds 3.0 T.

Abstract

We investigate the properties of quarks and gluons above the chiral phase transition temperature $T_c,$ using the RG improved gauge action and the Wilson quark action with two degenerate quarks mainly on a $32^3\times 16$ lattice. In the one-loop perturbation theory, the thermal ensemble is dominated by the gauge configurations with effectively $Z(3)$ center twisted boundary conditions, making the thermal expectation value of the spatial Polyakov loop take a non-trivial $Z(3)$ center. This is in agreement with our lattice simulation of high temperature QCD. We further observe that the temporal propagator of massless quarks at extremely high temperature $\beta=100.0 \, (T \simeq10^{58} T_c)$ remarkably agrees with the temporal propagator of free quarks with the $Z(3)$ twisted boundary condition for $t/L_t \geq 0.2$, but differs from that with the $Z(3)$ trivial boundary condition. As we increase the mass of quarks $m_q$, we find that the thermal ensemble continues to be dominated by the $Z(3)$ twisted gauge field configurations as long as $m_q \le 3.0 \, T$ and above that the $Z(3)$ trivial configurations come in. The transition is essentially identical to what we found in the departure from the conformal region in the zero-temperature many-flavor conformal QCD on a finite lattice by increasing the mass of quarks. We argue that the behavior is consistent with the renormalization group analysis at finite temperature.