We report progress toward computing the heavy quark momentum diffusion coefficient from the correlator of two chromoelectric fields attached to a Polyakov loop in pure SU(3) gauge theory. Using a multilevel algorithm and tree-level improvement, we study the behavior of the diffusion coefficient as a function of temperature in the wide range 1.1 < T=T c < 10 4 in order to compare it to perturbative expansions at high temperature. We find that within errors, the lattice results are remarkably compatible with the next-to-leading-order perturbative result.

We compute the running of the coupling in SU(2) gauge theory with six fermions in the fundamental representation of the gauge group. We find a strong evidence that this theory has an infrared stable fixed point at strong coupling and measure also the anomalous dimension of the fermion mass operator at the fixed point. This theory therefore likely lies close to the boundary of the conformal window and will display novel infrared dynamics if coupled with the electroweak sector of the Standard Model.

We study the evolution of the coupling in SU(2) gauge field theory with N f = 8 fundamental fermion flavors on the lattice. This model is expected to have an infrared fixed point at high coupling. We use HEX-smeared Wilson-clover action, and measure the gradient flow running coupling with Dirichlet boundary conditions. Extrapolating our results to continuum, we find an infrared fixed point at g 2 * = 8.24 (59) +0.97 −1.64 , with statistical and systematic error estimates. We also measure the anomalous dimension of the quark mass operator, and find its value at the fixed point γ * 0.15 ± 0.02, although for this quantity a reliable continuum limit is still lacking.