Sp (2N) Yang-Mills theories on the lattice: Scale setting and topology

We study Yang-Mills lattice theories with Sp(Nc) gauge group, with Nc=2N, for N=1,⋯,4. We show that if we divide the renormalized couplings appearing in the Wilson flow by the quadratic Casimir C2(F) of the Sp(Nc) group, then the resulting quantities display a good agreement among all values of Nc 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(Nc) theories, and extrapolate the results to the continuum limit for each Nc.