Charging the $\mathrm{O}\mathbf{(}N\mathbf{)}$ model

We determine, for the first time, the scaling dimensions of a family of fixed-charge operators stemming from the critical $O(N)$ model in $4-\epsilon$ dimensions to the leading and next to leading order terms in the charge expansion but to all orders in the coupling. We test our results to the maximum known order in perturbation theory while determining higher order terms.