Discretisation effects of gradient flows in QCD-like theories on the lattice

TL;DR

This paper investigates how discretisation effects influence topological properties and measurements in lattice QCD-like theories, highlighting differences between flow discretisations and estimating potential errors of about 10%.

Contribution

It provides a comparative analysis of Wilson and over-improved flow discretisations and assesses discretisation effects in large-scale lattice simulations of QCD-like theories.

Findings

Discretisation effects can be around 10% in current simulations.

Differences between Wilson and over-improved flows are quantitatively characterized.

Ratios of reference flow times help estimate discretisation impacts.

Abstract

Recent software advances now allow large-scale lattice studies of the Corrigan--Ramond large-$N_C$ limit of Yang-Mills theory coupled with a two-index antisymmetric fermion, providing a path to SUSY Yang-Mills. We are currently generating ensembles for $N_C=4,5,6$ for lattice spacings in the range $0.11 - 0.08$ fm. We report on two aspects of our work: the study of topological properties as well as estimates of discretisation effects. The first aspect is relevant since naively, fractional topological charges might be expected in our simulations. Using a gluonic definition of the topological charge combined with gradient flow, we perform an analysis of the effect of different discretisations of the kernel action, from which we identify and interpret quantitative differences between Wilson and over-improved flows such as DBW2. The second aspect is addressed by considering ratios of different reference flow times. We conclude that our current simulations might be affected by discretisation effects of order 10\%.