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

Understand

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.