Anomalous dimensions at large charge in d = 4 O ( N ) theory

Recently it was shown that the scaling dimension of the operator φn in λ(φφ)2 theory may be computed semiclassically at the Wilson-Fisher fixed point in d = 4 − ε, for generic values of λn, and this was verified to two loop order in perturbation theory at leading and subleading n . In subsequent work, this result was generalized to operators of fixed charge Q in O(N) theory and verified up to three loops in perturbation theory at leading and subleading Q. Here we extend this verification to four loops in O(N) theory, once again at leading and subleading Q. We also investigate the strong-coupling regime.