  Recently it was shown that the scaling dimension of the operator $\phi^n$ in
$\lambda(\bar\phi\phi)^2$ theory may be computed semiclassically 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
subleading $n$. This result was subsequently generalised to operators of fixed
charge $Q$ in $O(N)$ theory and verified up to four loops in perturbation
theory at leading and subleading $Q$. More recently, similar semiclassical
calculations have been performed for the classically scale-invariant
$U(N)\times U(N)$ theory in four dimensions, and verified up to two loops, once
again at leading and subleading $Q$. Here we extend this verification to four
loops. We also consider the corresponding classically scale-invariant theory in
three dimensions, similarly verifying the leading and subleading semiclassical
results up to four loops in perturbation theory.
