Anomalous dimensions at large charge in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> theory
I. Jack, D.R.T. Jones
Abstract
Recently it was shown that the scaling dimension of the operator ${\ensuremath{\phi}}^{n}$ in $\ensuremath{\lambda}(\overline{\ensuremath{\phi}}\ensuremath{\phi}{)}^{2}$ theory may be computed semiclassically at the Wilson-Fisher fixed point in $d=4\ensuremath{-}\ensuremath{\epsilon}$, for generic values of $\ensuremath{\lambda}n$, and this was verified to two loop order in perturbation theory at leading and subleading $n$. In subsequent work, this result was generalized to operators of fixed charge $\overline{Q}$ in $O(N)$ theory and verified up to three loops in perturbation theory at leading and subleading $\overline{Q}$. Here we extend this verification to four loops in $O(N)$ theory, once again at leading and subleading $\overline{Q}$. We also investigate the strong-coupling regime.