Charging the $O(N)$ model

Abstract

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.

6 pages. v2 Added the 4-loop anomalous dimension of spin-0 operators transforming in the traceless symmetric O(N) representations; corrected some formulae while the rest matches the PRD version