The gradient flow coupling in the Schr\"odinger Functional

TL;DR

This paper investigates the perturbative properties of the Yang-Mills gradient flow within the Schr"odinger Functional framework, assessing its effectiveness for defining a precise, low-cutoff effect running coupling in lattice gauge theory.

Contribution

It provides a perturbative analysis of the gradient flow coupling in the Schr"odinger Functional and demonstrates its suitability for high-precision continuum limit studies.

Findings

Cutoff effects are modest at leading order in perturbation theory.

The coupling shows high statistical precision on Nf=2 ensembles.

The method is suitable for precise continuum limit extrapolations.

Abstract

We study the perturbative behavior of the Yang-Mills gradient flow in the Schr\"odinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the size of the finite volume box. From our perturbative computation we estimate the size of cutoff effects of this coupling to leading order in perturbation theory. On a set of Nf=2 gauge field ensembles in a physical volume of L ~ 0.4 fm we finally demonstrate the suitability of the coupling for a precise continuum limit due to modest cutoff effects and high statistical precision.