Shear and bulk viscosities of gluon plasma across the transition temperature from lattice QCD

TL;DR

This paper computes the shear and bulk viscosities of SU(3) Yang–Mills theory across $0.76\,T_c$ to $2.25\,T_c$ using high-precision lattice QCD with gradient flow and a blocking technique to obtain energy–momentum tensor correlators at percent-level accuracy. By performing continuum extrapolations on three large lattices and constraining the spectral reconstruction with a next-to-leading-order perturbative UV input while modeling the IR with a Lorentzian transport peak, the authors extract $\eta$ and $\zeta$ from Kubo relations. They find $\eta/s$ exhibits a minimum near the transition temperature and rises for $T>T_c$, whereas $\zeta/s$ decreases monotonically over the studied range; at high temperatures, $\eta/s$ approaches perturbative predictions. The work demonstrates a controlled, nonperturbative determination of transport coefficients in the gluon plasma and provides a benchmark for comparisons with analytic models and phenomenology, with a natural path toward extending to full QCD with dynamical quarks.

Abstract

We investigate the temperature dependence of the shear viscosity ($η$) and bulk viscosity ($ζ$) of the gluon plasma using lattice QCD over the range 0.76--2.25 $T_c$, extending from below the transition temperature $T_c$ across the transition region and into the deconfined phase. At each temperature, we employ three large, fine lattices, which enables controlled continuum extrapolations of the energy-momentum tensor correlators. Using gradient flow together with a recently developed blocking technique, we achieve percent level precision for these correlators, providing strong constraints for a model-based spectral analysis. Since the inversion to real-time information is intrinsically ill posed, we extract viscosities by fitting spectral functions whose ultraviolet behavior is matched to the best available perturbative result, while the infrared region is described by a Lorentzian transport peak. The dominant modeling uncertainty associated with the transport-peak width is bracketed by varying it over a physically motivated range set by thermal scales. We find that the shear-viscosity-to-entropy-density ratio, $η/s$, exhibits a minimum near the transition temperature $T_c$ and increases for $T>T_c$, whereas the bulk-viscosity-to-entropy-density ratio, $ζ/s$, decreases monotonically over the entire temperature range studied.

Figures (10)

• Figure 1: Top: continuum extrapolation of $c_1$ (left) and $c_2$ (right) using Ansätze Eq. (\ref{['eq:c1_to_0']}). Bottom: a comparison of $c_1$ (left) measured at finite lattice spacings and in the continuum limit and the same for $c_2$ (right).
• Figure 2: Continuum extrapolation of the bare EMT correlator in the shear channel at $\sqrt{8 \tau_{\mathrm{F}}} / \tau = 0.520$ and $T=0.9 \,T_c$ via a joint fit with the Ansätze in Eq. (\ref{['eq:joints']}).
• Figure 3: Left: flow-time extrapolation for the shear-channel correlators at $T=1.5\,T_c$. Right: same as the left panel but for the bulk channel.
• Figure 4: Left: shear-channel correlators after the double extrapolation for all temperatures. Right: same as the left panel but for the bulk channel.
• Figure 5: The dependence of $\eta/T^3$ on $\Delta$ at $0.76\,T_c$ with $C=1$.