The gradient flow running coupling scheme

TL;DR

This paper introduces a running coupling scheme based on the Yang-Mills gradient flow in finite volume, calculating the discrete beta-function for SU(3) gauge theory with four fermions, and compares it with perturbative results.

Contribution

It presents a novel scheme for defining the running coupling using gradient flow and provides non-perturbative calculations of the beta-function for specific gauge theories.

Findings

Agreement with perturbative results at small coupling

Continuum extrapolation performed for lattice data

Brief discussion on SU(2) gauge group case

Abstract

The Yang-Mills gradient flow in finite volume is used to define a running coupling scheme. As our main result the discrete beta-function, or step scaling function, is calculated for scale change s=3/2 at several lattice spacings for SU(3) gauge theory coupled to N_f = 4 fundamental massless fermions. The continuum extrapolation is performed and agreement is found with the continuum perturbative results for small renormalized coupling. The case of SU(2) gauge group is briefly commented on.