Recently it was shown that the scaling dimension of the operator ${\varphi }^n$ 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.

• Received 24 July 2020
• Accepted 18 September 2020

DOI:https://doi.org/10.1103/PhysRevD.102.085012

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Published by the American Physical Society