  We consider a 4d scalar field coupled to large $N$ free or critical $O(N)$
vector models, either bosonic or fermionic, on a 3d boundary. We compute the
$\beta$ function of the classically marginal bulk/boundary interaction at the
first non-trivial order in the large $N$ expansion and exactly in the coupling.
Starting with the free (critical) vector model at weak coupling, we find a
fixed point at infinite coupling in which the boundary theory is the critical
(free) vector model and the bulk decouples. We show that a strong/weak duality
relates one description of the renormalization group flow to another one in
which the free and the critical vector models are exchanged. We then consider
the theory with an additional Maxwell field in the bulk, which also gives
decoupling limits with gauged vector models on the boundary.
