We calculate shear viscosity and bulk viscosity in <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> gauge theory on the lattice at <math><mn>1.5</mn><msub><mi>T</mi><mi>c</mi></msub></math>. 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 <math><mrow><mi>η</mi><mo>/</mo><mi>s</mi><mo>=</mo><mn>0.15</mn><mi>–</mi><mn>0.48</mn></mrow></math> and <math><mi>ζ</mi><mo>/</mo><mi>s</mi><mo>=</mo><mn>0.017</mn><mi>–</mi><mn>0.059</mn></math>.

Germany

Luis Altenkort

Alexander M. Eller

Taiwan

Anthony Francis

Olaf Kaczmarek

Lukas Mazur

Guy D. Moore

Hai-Tao Shu

Viscosity of pure-glue QCD from the lattice

We propose a method to substantially improve the signal-to-noise ratio of lattice correlation functions for bosonic operators or other operator combinations with disconnected contributions. The technique is applicable for correlations between operators on two planes (zero momentum correlators) when the dimension of the plane is larger than the separation between the two planes which are correlated. In this case, the correlation arises primarily from points whose in-plane coordinates are close, but noise arises from all pairs of points. By breaking each plane into bins and computing bin-bin correlations, it is possible to capture these short-distance correlators exactly while replacing (small) correlators at large spatial extent with a fit, with smaller uncertainty than the data. The cost is only marginally larger than averaging each plane before correlating, but the improvement in signal-to-noise can be substantial. We test the method on correlators of the gradient-flowed topological charge density and squared field strength, finding noise reductions by a factor of <math><mrow><mo>∼</mo><mn>3</mn><mi>–</mi><mn>7</mn></mrow></math> compared to the conventional approach on the same ensemble of configurations.

O. Kaczmarek

Lattice QCD noise reduction for bosonic correlators through blocking

The finite temperature phase diagram of QCD with two massless quark flavors is not yet understood because of the subtle effects of anomalous <math><msub><mi>U</mi><mi>A</mi></msub><mo>(</mo><mn>1</mn><mo>)</mo></math> symmetry. In this work we address this issue by studying the fate of the anomalous <math><msub><mi>U</mi><mi>A</mi></msub><mo>(</mo><mn>1</mn><mo>)</mo></math> symmetry in <math><mn>2</mn><mo>+</mo><mn>1</mn></math> flavor QCD just above the chiral crossover transition temperature <math><msub><mi>T</mi><mi>c</mi></msub></math>, lowering the light quark mass toward the chiral limit along the line of constant physical strange quark mass. We use the gauge configurations generated using the highly improved staggered quark discretization on lattice volumes <math><msup><mn>32</mn><mn>3</mn></msup><mo>×</mo><mn>8</mn></math> and <math><msup><mn>56</mn><mn>3</mn></msup><mo>×</mo><mn>8</mn></math> to study the renormalized eigenvalue spectrum of QCD with a valence overlap Dirac operator. We implement new numerical techniques that allow us to measure about 100–200 eigenvalues of the gauge ensembles with light quark masses <math><mo>≳</mo><mn>0.6</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. From a detailed analysis of the dependence of the renormalized eigenvalue spectrum and <math><msub><mi>U</mi><mi>A</mi></msub><mo>(</mo><mn>1</mn><mo>)</mo></math> breaking observables on the light quark mass, our study suggests <math><msub><mi>U</mi><mi>A</mi></msub><mo>(</mo><mn>1</mn><mo>)</mo></math> is broken at <math><mi>T</mi><mo>≳</mo><msub><mi>T</mi><mi>c</mi></msub></math> even when the chiral limit is approached.

China

India

Sayantan Sharma

Eigenvalue spectra of QCD and the fate of <math><msub><mi>U</mi><mi>A</mi></msub><mo>(</mo><mn>1</mn><mo>)</mo></math> breaking towards the chiral limit

We show how the sphaleron rate (the Minkowski rate for topological charge diffusion) can be determined by analytical continuation of the Euclidean topological-charge-density two-point function, which we investigate on the lattice, using gradient flow to reduce noise and provide improved operators which more accurately measure topology. We measure the correlators on large, fine lattices in the quenched approximation at <math><mn>1.5</mn><msub><mi>T</mi><mi>c</mi></msub></math> with high precision. Based on these data we first perform a continuum extrapolation at fixed physical flow time and then extrapolate the continuum estimates to zero flow time. The extrapolated correlators are then used to study the sphaleron rate by spectral reconstruction based on perturbatively motivated models.

H.T. Shu

Sphaleron rate from Euclidean lattice correlators: An exploration

We apply the gradient flow on a color-electric two-point function that encodes the heavy quark momentum diffusion coefficient. The simulations are done on fine isotropic lattices in the quenched approximation at <math><mrow><mn>1.5</mn><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math>. The continuum extrapolation is performed at fixed flow time followed by a second extrapolation to zero flow time. Perturbative calculations of this correlation function under Wilson flow are used to enhance the extrapolations of the nonperturbative lattice correlator. The final estimate for the continuum correlator at zero flow time largely agrees with one obtained from a previous study using the multilevel algorithm. We perform a spectral reconstruction based on perturbative model fits to estimate the heavy quark momentum diffusion coefficient. The approach we present here yields high-precision data for the correlator and is also applicable for actions with dynamical fermions.

Heavy quark momentum diffusion from the lattice using gradient flow

In this work, we consider open-boundary conditions at high temperatures, as they can potentially be of help to measure the topological susceptibility. In particular, we measure the extent of the boundary effects at $$T=1.5T_c$$ <math><mrow><mi>T</mi><mo>=</mo><mn>1.5</mn><msub><mi>T</mi><mi>c</mi></msub></mrow></math>  and $$T=2.7T_c$$ <math><mrow><mi>T</mi><mo>=</mo><mn>2.7</mn><msub><mi>T</mi><mi>c</mi></msub></mrow></math> . In the first case, it is larger than at $$T=0$$ <math><mrow><mi>T</mi><mo>=</mo><mn>0</mn></mrow></math>  while we find it to be smaller in the second case. The length of this “boundary zone” is controlled by the screening masses. We use this fact to measure the scalar and pseudo-scalar screening masses at these two temperatures. We observe a mass gap at $$T=1.5T_c$$ <math><mrow><mi>T</mi><mo>=</mo><mn>1.5</mn><msub><mi>T</mi><mi>c</mi></msub></mrow></math>  but not at $$T=2.7T_c$$ <math><mrow><mi>T</mi><mo>=</mo><mn>2.7</mn><msub><mi>T</mi><mi>c</mi></msub></mrow></math> . Finally, we use our pseudo-scalar channel analysis to estimate the topological susceptibility. The results at $$T=1.5T_c$$ <math><mrow><mi>T</mi><mo>=</mo><mn>1.5</mn><msub><mi>T</mi><mi>c</mi></msub></mrow></math>  are in good agreement with the literature. At $$T=2.7T_c$$ <math><mrow><mi>T</mi><mo>=</mo><mn>2.7</mn><msub><mi>T</mi><mi>c</mi></msub></mrow></math> , they appear to suffer from topological freezing, which prevents us from providing a precise determination of the topological susceptibility.