Correlators of Large N Fermionic Chern-Simons Vector Models

Abstract

We consider the large N limit of three-dimensional U(N)_k Chern-Simons theory coupled to a Dirac fermion in the fundamental representation. In this limit, we compute several correlators to all orders in the `t Hooft coupling N/k. It was suggested recently that this theory is dual to the Legendre-transformed theory of scalar fields coupled to Chern-Simons gauge interactions. Our results show that this duality holds for any value of the `t Hooft coupling, at least at the level of the planar 3-point functions. In addition, we determine the sign in the duality transformation of the Chern-Simons level, as well as the relation between the "triple-trace" deformation which exists in the bosonic Chern-Simons theory and in the Legendre-transformed fermionic theory.