Smoothing properties of the Wilson flow and the topological charge

TL;DR

This paper investigates the smoothing properties of the Wilson flow in lattice gauge theories, demonstrating that overimproved gauge actions stabilize topological charge measurements more effectively than standard Wilson flow.

Contribution

It introduces the use of overimproved gauge actions in the Wilson flow to better stabilize topological charge in lattice simulations.

Findings

Overimproved gauge actions stabilize topological charge at moderate flow times.

Standard Wilson flow does not stabilize topological charge as effectively.

Fractional topological charges are studied in SU(4) ensembles.

Abstract

We study SU$(N_C)$ gauge theories with a single fermion in the two-index antisymmetric representation to predict the mesonic spectrum of supersymmetric $\mathcal{N}=1$ SYM theories. Using gradient flow methods, we investigate fractional topological charges in $N_C = 4$ ensembles with varying lattice spacings. We show that the use of overimproved gauge actions (specifically the DBW2 action) in the smearing kernel stabilises the values of the topological charge already at moderate values of the flow time, while this is not the case for the standard Wilson flow.