Anomalous dimensions for $\phi^n$ in scale invariant $d=3$ theory

TL;DR

This paper extends the semiclassical computation of anomalous dimensions for operators in a scale-invariant 3D theory to six loops, verifies results at higher orders, and explores strong-coupling behavior in an $O(N)$ symmetric model.

Contribution

It provides a six-loop verification of semiclassical predictions for anomalous dimensions and analyzes the strong-coupling regime in an $O(N)$ scalar theory.

Findings

Six-loop verification of semiclassical results

Extension to $O(N)$ symmetric scalar theory

Insights into strong-coupling behavior

Abstract

Recently it was shown that the scaling dimension of the operator $\phi^n$ in scale-invariant $d=3$ theory may be computed semiclassically, and this was verified to leading order (two loops) in perturbation theory at leading and subleading $n$. Here we extend this verification to six loops, once again at leading and subleading $n$. We then perform a similar exercise for a theory with a multiplet of real scalars and an $O(N)$ invariant hexic interaction. We also investigate the strong-coupling regime for this example.