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

Abstract

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

Comments: 16 pages. 6 Figures. Typos corrected; references and an acknowledgement added. Some minor errors corrected in a figure and equations