Anomalous dimensions in CFT with weakly broken higher spin symmetry

TL;DR

This paper presents a method to calculate anomalous dimensions of broken higher spin currents in weakly broken higher spin symmetric conformal field theories, with applications to various models and dimensions.

Contribution

It introduces an efficient approach based on classical non-conservation equations to determine anomalous dimensions in weakly broken higher spin theories.

Findings

Derived anomalous dimensions for higher spin currents in multiple models.

Provided estimates for higher spin operator dimensions in 3D $O(N)$ models.

Applied the method to models in various dimensions including $d=4-psilon$ and $d=2+psilon$.

Abstract

In a conformal field theory with weakly broken higher spin symmetry, the leading order anomalous dimensions of the broken currents can be efficiently determined from the structure of the classical non-conservation equations. We apply this method to the explicit example of $O(N)$ invariant scalar field theories in various dimensions, including the large $N$ critical $O(N)$ model in general $d$, the Wilson-Fisher fixed point in $d=4-\epsilon$, cubic scalar models in $d=6-\epsilon$ and the nonlinear sigma model in $d=2+\epsilon$. Using information from the $d=4-\epsilon$ and $d=2+\epsilon$ expansions, we obtain some estimates for the dimensions of the higher spin operators in the critical 3d $O(N)$ models for a few low values of $N$ and spin.