A test of bosonization at the level of four-point functions in Chern-Simons vector models

We study four-point functions in Chern-Simons vector models in the large N limit. We compute the four-point function of the scalar primary to all orders in the 't Hooft coupling lambda = N/k in U ( N) k Chern-Simons theory coupled to a fundamental fermion, in both the critical and non-critical theory, for a particular case of the external momenta. These theories cover the entire 3-parameter quasi-boson and 2-parameter quasi-fermion families of 3-dimensional quantum field theories with a slightly-broken higher spin symmetry. Our results are consistent with the celebrated bosonization duality, as we explicitly verify by calculating four-point functions in the free critical and non-critical bosonic theories.