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

TL;DR

This study explores SU(3) Yang Mills theory at very short distances using fine lattice spacings and gradient flow techniques, aiming to understand the theory's behavior and extract fundamental parameters.

Contribution

It demonstrates the feasibility of small flow-time expansion and the extraction of the b1b4-parameter from lattice simulations at unprecedented small distances.

Findings

Deviations from 4-loop perturbative b2-function at b1b4d0.2

Successful extrapolation of b1b4-parameter to small distances

Lattice spacings down to 0.015 fm used with open boundary conditions

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 $r_0\Lambda$.