D = 3 bosonic vector models coupled to Chern-Simons gauge theories

We study three dimensional O(N)k and U(N)k Chern-Simons theories coupled to a scalar field in the fundamental representation, in the large N limit. For infinite k this is just the singlet sector of the O(N) (U(N)) vector model, which is conjectured to be dual to Vasiliev's higher spin gravity theory on AdS ₄. For large k and N we obtain a paritybreaking deformation of this theory, controlled by the 't Hooft coupling λ = 4πN=k. For infinite N we argue (and show explicitly at two-loop order) that the theories with finite λ are conformally invariant, and also have an exactly marginal (φ ²) ³ deformation. For large but finite N and small 't Hooft coupling λ, we show that there is still a line of fixed points parameterized by the 't Hooft coupling λ. We show that, at infinite N, the interacting non-parity-invariant theory with finite λ has the same spectrum of primary operators as the free theory, consisting of an infinite tower of conserved higher-spin currents and a scalar operator with scaling dimension λ = 1; however, the correlation functions of these operators do depend on λ. Our results suggest that there should exist a family of higher spin gravity theories, parameterized by λ, and continuously connected to Vasiliev's theory. For finite N the higher spin currents are not conserved.