<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>p</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> Yang-Mills theories on the lattice: Scale setting and topology

Abstract

We study Yang-Mills lattice theories with $Sp({N}_{c})$ gauge group, with ${N}_{c}=2N$, for $N=1,\dots{},4$. We show that if we divide the renormalized couplings appearing in the Wilson flow by the quadratic Casimir ${C}_{2}(F)$ of the $Sp({N}_{c})$ group, then the resulting quantities display a good agreement among all values of ${N}_{c}$ considered, over a finite interval in flow time. We use this scaled version of the Wilson flow as a scale-setting procedure, compute the topological susceptibility of the $Sp({N}_{c})$ theories, and extrapolate the results to the continuum limit for each ${N}_{c}$.

Topics & Concepts