Anomalous dimensions at large charge for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>×</mml:mo><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> theory in three and four dimensions

Recently it was shown that the scaling dimension of operator $\phi^n$ in $\lambda(\bar\phi\phi)^2$ theory may be computed semiclassically at Wilson-Fisher fixed point $d=4-\epsilon$, for generic values $\lambda n$, and this verified to two loop order perturbation leading subleading $n$. This result subsequently generalised operators charge $Q$ $O(N)$ up four loops $Q$. More recently, similar semiclassical calculations have been performed classically scale-invariant $U(N)\times U(N)$ dimensions, loops, once again Here we extend verification loops. We also consider corresponding three similarly verifying results theory.