Anomalous dimensions in CFT with weakly broken higher spin symmetry

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 - is an element of, cubic scalar models in d = 6 - is an element of and the nonlinear sigma model in d = 2 + is an element of. Using information from the d - 4 - is an element of and d = 2 + is an element of 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.