SU(3) Yang Mills theory at small distances and fine lattices

Abstract

We investigate the SU(3) Yang Mills theory at small gradient flow time and at short distances. Lattice spacings down to $a=0.015$ fm are simulated with open boundary conditions to allow topology to flow in and out. We study the behaviour of the action density $E(t)$ close to the boundaries, the feasibility of the small flow-time expansion and the extraction of the $\Lambda$-parameter from the static force at small distances. For the latter, significant deviations from the 4-loop perturbative $\beta$-function are visible at $\alpha \approx 0.2$. We still can extrapolate to extract $r_0\Lambda$.

Comments: 8 pages, 5 figures, Proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain