Topological susceptibility, scale setting and universality from $Sp(N_c)$ gauge theories

TL;DR

This study investigates the topological properties of $Sp(N_c)$ gauge theories using Wilson flow, revealing scaling behaviors and proposing a universal large-$N_c$ limit for topological susceptibility across different gauge groups.

Contribution

It is the first comprehensive analysis of Wilson flow and topological susceptibility in $Sp(N_c)$ gauge theories, establishing their scaling and universality properties.

Findings

Wilson flow scales $t_0$ and $w_0$ scale with the quadratic Casimir.

The continuum topological susceptibility scales with the group dimension.

A universal large-$N_c$ limit of the rescaled susceptibility is proposed.

Abstract

In this contribution, we report on our study of the properties of the Wilson flow and on the calculation of the topological susceptibility of $Sp(N_c)$ gauge theories for $N_c=2,\,4,\,6,\,8$. The Wilson flow is shown to scale according to the quadratic Casimir operator of the gauge group, as was already observed for $SU(N_c)$, and the commonly used scales $t_0$ and $w_0$ are obtained for a large interval of the inverse coupling for each probed value of $N_c$. The continuum limit of the topological susceptibility is computed and we conjecture that it scales with the dimension of the group. The lattice measurements performed in the $SU(N_c)$ Yang-Mills theories by several independent collaborations allow us to test this conjecture and to obtain a universal large-$N_c$ limit of the rescaled topological susceptibility.