We calculate shear viscosity and bulk viscosity in $SU(3)$ gauge theory on the lattice at $1.5T_c$. The viscosities are extracted via a Kubo formula from the reconstructed spectral function which we determine from the Euclidean time dependence of the corresponding channel of the energy-momentum tensor correlators. We obtain unprecedented precision for the correlators by applying gradient-flow and blocking methods. The correlators are extrapolated to the continuum and then to zero-flow time. To extract the viscosities we fit theoretically inspired models to the lattice data and cross-check the fit results using the Backus-Gilbert method. The final estimates for shear and bulk viscosity are $\eta /s=0.15–0.48$ and $\zeta /s=0.017–0.059$.

• Received 28 November 2022
• Accepted 22 June 2023

DOI:https://doi.org/10.1103/PhysRevD.108.014503

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Published by the American Physical Society