$Sp(2N)$ 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 $N=1,\cdots ,4$. We show that if we divide the renormalised 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 $N_c$.

Comments: 19 pages, 17 figures. v4: Typos corrected in eq. 35, Figures 3 and 4. Results unchanged