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-ϵ, cubic scalar models in d=6-ϵ and the nonlinear sigma model in d=2+ϵ.

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... ing information from the d=4-ϵ and d=2+ϵ 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.