{Scale setting of SU(N) Yang{\textendash}Mills theory, topology and large-N volume independence}

We set the scale of SUðNÞ Yang-Mills theories for N ¼ 3, 5, 8 and in the large-N limit via gradient flow, as a first step towards the computation of the large-N Λ-parameter using step scaling. We adopt twisted boundary conditions to achieve large-N volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as ∼0.025 fm for all the explored values of N, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-N twisted volume reduction.