Gauge field smearing and controlled continuum extrapolations

TL;DR

This paper examines how gauge field smearing, especially via gradient flow, affects continuum extrapolations in lattice gauge theories, emphasizing the importance of controlled smearing to preserve physical behavior.

Contribution

It analyzes the impact of smearing and physical flow on continuum scaling, comparing gradient flow and stout smearing in pure gauge theories.

Findings

Proper smearing preserves continuum scaling behavior.

Gradient flow and stout smearing can be effectively compared.

Uncontrolled smearing leads to distorted continuum limits.

Abstract

When designing lattice actions, gauge field smearing is often used in the definition of the lattice Dirac operator. Too much smearing can result in uncontrolled continuum extrapolations as the short distance behaviour of the theory is mutilated, which is a situation to be avoided. As a smearing prescription we focus on the gradient flow formalism as it allows to study both smearing and physical flow simultaneously. We investigate the effect of smearing and physical flow on the scaling towards the continuum limit in pure gauge theory. We focus on the example of Creutz ratios, which provide a measure of the physical forces felt by the fermions. For suitable smearing strengths we further investigate the impact of replacing the Wilson gradient flow by stout smearing.