Through a careful study of smooth Wilson loop operators on the lattice, we are able to obtain very accurate confirmation of the $1/N^2$ scaling predicted by `t Hooft for the pure $\mathrm{SU}(N)$ gauge theory. We present our results for Wilson loops smoothed with the Yang-Mills gradient flow and matched through the scale $t_0$. This allows us to have renormalizable operators and test the $1/N^2$ scaling both at finite lattice spacing and in the continuum. Our results show an excellent scaling up to $1/N = 1/3$. Additionally, we look into the property of factorization in the large $N$ limit, and obtain very precise non-perturbative evidence of its validity.

Theoretical Developments