Influence of topology on the scale setting

TL;DR

This paper explores how the topology influences scale setting in lattice gauge theories using Wilson flow, demonstrating its effectiveness in supersymmetric Yang-Mills theory and revealing correlations between scale and topological charge.

Contribution

It extends the Wilson flow scale setting method to N=1 supersymmetric Yang-Mills theory and investigates the relationship between the scale and topological charge.

Findings

Topological charge approaches integer values with increasing flow time.

Topological susceptibility tends to zero in the chiral limit.

A correlation exists between the Wilson flow scale and topological charge.

Abstract

Recently a new method to set the scale in lattice gauge theories, based on the gradient flow generated by the Wilson action, has been proposed, and the systematic errors of the new scales t0 and w0 have been investigated by various groups. The Wilson flow provides also an interesting alternative smoothing procedure in particular useful for the measurement of the topological charge as a pure gluonic observable. We show the viability of this method for N=1 supersymmetric Yang-Mills theory by analysing the configurations produced by the DESY-Muenster collaboration. For increasing flow time the topological charge quickly approaches near-integer values. The topological susceptibility has been measured for different fermion masses and its value is observed to approach zero in the chiral limit. Finally, the relation between the scale defined by the Wilson flow and the topological charge has been investigated, demonstrating a correlation between these two quantities.