Shear viscosity from quenched to full lattice QCD

TL;DR

This work addresses the lattice determination of the shear viscosity to entropy ratio $η/s$ in full QCD, a challenging problem due to the ill‑posed analytic continuation from Euclidean correlators and the nontrivial renormalization of the energy–momentum tensor. The authors deploy gradient flow to construct renormalized $T_{μν}$ operators and develop a two‑coefficient renormalization strategy, $Z_1$ and $Z_3$, requiring two independent inputs. By exploiting imaginary isospin chemical potential and the Roberge–Weiss transition, they generate two ensembles that isolate fermionic and gluonic contributions, enabling independent constraints on the renormalization coefficients via $ε+p = ⟨T_{xx}-T_{00}⟩$. Preliminary lattice results at $β=7.373$ show the method can differentiate the ensembles and quantify the fermionic vs gluonic contributions, with a plan to perform continuum extrapolation and ultimately extract $η$ from the spectral function while controlling systematic uncertainties.

Abstract

The shear viscosity of the quark-gluon plasma (QGP) plays a crucial role in interpreting current measurements from heavy-ion collisions and is a key input to hydro-dynamical models. The interest in shear viscosity also lies in the fact that QGP is the most ideal fluid ever observed and has the shear viscosity to entropy ratio ($η/ s$) close to the theoretical bound $η/ s \geq 1/ 4 π$ in the strong coupling region within AdS/CFT formalism. The lattice determination of $η/ s$ has been explored for the pure gauge case, but its determination in full QCD remains unexplored, despite its significant importance. In this proceeding, we present updates on extending our quenched findings to full QCD. Specifically, we focus on the renormalization of the energy-momentum tensor with the gradient flow method and provide a progress update on determining the relevant renormalization coefficients for shear viscosity. For this purpose, we have used an imaginary isospin chemical potential.

Figures (3)

• Figure 1: (Left) Possible Polyakov loop vacua $V_{1,2,3}$, and the quark twist angles for the Roberge-Weiss case (red) and our case (black). (Right) Free fermionic pressure for the Polyakov-loop vacua $V_1$, $V_2$ and $V_3$.
• Figure 2: (Left) The fermionic contribution for trace anomaly. (Right) Gluonic and fermionic contribution to trace anomaly.
• Figure 3: (Left) The number density plot for $u$, $d$ and $s$ flavors. (Right) The enthalpy density with imaginary isospin chemical potential.