  Using an explicit path integral approach we derive non-abelian bosonization
and duality of 3D systems in the large $N$ limit. We first consider a fermionic
$U(N)$ vector model coupled to level $k$ Chern-Simons theory, following
standard techniques we gauge the original global symmetry and impose the
corresponding field strength $F_{\mu\nu}$ to vanish introducing a Lagrange
multiplier $\Lambda$. Exchanging the order of integrations we obtain the
bosonized theory with $\Lambda$ as the propagating field using the large $N$
rather than the previously used large mass limit. Next we follow the same
procedure to dualize the scalar $U(N)$ vector model coupled to Chern-Simons and
find its corresponding dual theory. Finally, we compare the partition functions
of the two resulting theories and find that they agree in the large $N$ limit
including a level/rank duality. This provides a constructive evidence for
previous proposals on level/rank duality of 3D vector models in the large $N$
limit. We also present a partial analysis at subleading order in large $N$ and
find that the duality does not generically hold at this level.
