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Lattice simulations of Yang-Mills theories coupled with $N_f$ flavours offermions in the adjoint representation provide a way to probe thenon-perturbative regime of a plethora of different physical scenarios, such asSupersymmetric Yang-Mills theory to BSM models. We are interested in thelarge-$N_c$ limit of these theories, for which standard lattice techniques arelimited by high-computational costs. Our approach makes use of thewell-established twisted volume reduction, which allows one to simulate thesetheories on a $1^4$ lattice. In this talk, we are going to present a detailedstudy of the scale setting of these theories, performed with Wilson flowtechniques, but endowed with a procedure that allowed us to reducefinite-volume (finite $N_c$) systematic effects. We will apply this procedureto our configurations for $N_f=0,\frac{1}{2},1,2$ and analyze the dependence ofthe scale on the coupling, the adjoint fermion mass and the number of flavours.For the cases in which enough couplings are available we compared the resulting$\beta$-function with the predictions of perturbation theory, finding very goodagreement.

Adjoint fermions at large-N on the lattice