Chern-Simons gauge theories coupled to massless fundamental scalars or fermions define interesting non-supersymmetric 3d CFTs that possess approximate higherspin 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.

Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points [1]. These theories, particularly those based on bifundamental matter, are important because they may provide simple non-supersymmetric examples of the AdS/CFT correspondence. For instance, it seems natural to conjecture that O(N ) −k × O(N ) k Chern-Simons theory coupled to Majorana fermions transforming in a bi-vector representation may be dual to pure Einstein gravity with a small negative cosmological constant in the "M-theory" limit where k = 1 and N is large. While it is extremely difficult to directly study such bifundamental theories when k = 1 or even at strong 't Hooft coupling λ = N k , it is possible to calculate physical quantities to all orders in λ in a U (M ) k M × U (N ) k N theory, in the limit M N , in an M/N expansion. To illustrate this, we calculate the anomalous dimension of the primary operator trψψ, to first order in M/N , to all orders in λ M = N k M , but with λ N = N k N = 0. We also comment on possible bosonization dualities for bifundamental Chern-Simons theories.

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