Anomalous dimensions at large charge for $U(N)\times U(N)$ theory in three and four dimensions

Abstract

Recently it was shown that the scaling dimension of the operator $\ddot{I}{•}^n$ in $\hat{I}»(\bar{\ddot{I}}•\ddot{I}•{)}^2$ theory may be computed semiclassically at the Wilson-Fisher fixed point in $d=4-\hat{I}\mu$, for generic values of $\hat{I}»n$, 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.

8 figures, 5 tables, 24 pages. arXiv admin note: text overlap with arXiv:2101.09820