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

TL;DR

This paper extends the perturbative verification of anomalous dimensions at large charge in $O(N)$ theories up to four loops and explores the strong-coupling regime, enhancing understanding of operator scaling at the Wilson-Fisher fixed point.

Contribution

It provides a four-loop perturbative verification of anomalous dimensions at large charge in $O(N)$ theories and investigates the strong-coupling behavior.

Findings

Verification up to four loops at leading and sub-leading order.

Extension to strong-coupling regime analysis.

Confirmation of previous perturbative results at higher loop order.

Abstract

Recently it was shown that the scaling dimension of the operator $\phi^n$ in $\lambda(\phi^*\phi)^2$ theory may be computed semi-classically 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 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.