Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions

We consider the conformal field theory of N complex massless scalars in 2 + 1 dimensions, coupled to a U(N) Chern-Simons theory at level k. This theory has a 't Hooft large N limit, keeping fixed λ ≡ N/k. We compute some correlation functions in this theory exactly as a function of λ, in the large N (planar) limit. We show that the results match with the general predictions of Maldacena and Zhiboedov for the correlators of theories that have high-spin symmetries in the large N limit. It has been suggested in the past that this theory is dual (in the large N limit) to the Legendre transform of the theory of fermions coupled to a Chern-Simons gauge field, and our results allow us to find the precise mapping between the two theories. We find that in the large N limit the theory of N scalars coupled to a U(N) _k Chern-Simons theory is equivalent to the Legendre transform of the theory of k fermions coupled to a U(k) _N Chern-Simons theory, thus providing a bosonization of the latter theory. We conjecture that perhaps this duality is valid also for finite values of N and k, where on the fermionic side we should now have (for N _f flavors) a U(k)N-{N_f/2 theory. Similar results hold for real scalars (fermions) coupled to the O(N) _k Chern-Simons theory.