Dualities in 3D large N vector models

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 μν to vanish introducing a lagrange multiplier λ. exchanging the order of integrations we obtain the bosonized theory with λ 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.