ANOMALOUS DIMENSIONS AT LARGE CHARGE IN d=4 O(N) THEORY

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