Comparison of smoothening flows for the topological charge in QCD-like theories

We investigate properties of the topological charge for several <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:msub><a:mi>N</a:mi><a:mi>C</a:mi></a:msub><a:mo stretchy="false">)</a:mo></a:math> gauge field ensembles for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>N</e:mi><e:mi>C</e:mi></e:msub><e:mo>=</e:mo><e:mn>4</e:mn></e:math>, 5, 6 with a single fermion in the two-index antisymmetric representation, covering multiple lattice spacings at otherwise approximately constant physical parameters. Comparing the topological charge defined by the Wilson flow and the overimproved DBW2 flow we find that already at small flow times the latter stabilizes on discrete values. We provide evidence that as the lattice spacing is lowered the Wilson flow also separates into discrete sectors at earlier flow times. Adopting the DBW2 definition in the remainder of the analysis, we do not see any evidence of fractional topological charges, which could in principle appear at finite lattice spacing.