  Chern-Simons gauge theories coupled to massless fundamental scalars or
fermions define interesting non-supersymmetric 3d CFTs that possess approximate
higher-spin symmetries at large N. In this paper, we compute the scaling
dimensions of the higher-spin operators in these models, to leading order in
the 1/N expansion and exactly in the 't Hooft coupling. We obtain these results
in two independent ways: by using conformal symmetry and the classical
equations of motion to fix the structure of the current non-conservation, and
by a direct Feynman diagram calculation. The full dependence on the 't Hooft
coupling can be restored by using results that follow from the weakly broken
higher-spin symmetry. This analysis also allows us to obtain some explicit
results for the non-conserved, parity-breaking structures that appear in planar
three-point functions of the higher-spin operators. At large spin, we find that
the anomalous dimensions grow logarithmically with the spin, in agreement with
general expectations. This logarithmic behavior disappears in the strong
coupling limit, where the anomalous dimensions turn into those of the critical
O(N) or Gross-Neveu models, in agreement with the conjectured 3d bosonization
duality.
