  For W_N minimal model CFT's at Large N, we formulate a nonlinear field theory
of primary operators. A classification of single-trace operators is given first
based on which an interacting field theory operating in Fock space is built. A
hamiltonian is constructed with the property that it reproduces exactly the
spectrum of conformal dimensions of all the primaries. This field theory is
characterized by cubic (and quartic) interactions with G=1/N as an interaction
parameter. It is seen that the 1/N nonlinear representation contains the
interactions and structure known from Matrix-vector models.
