  Three dimensional, $U(N)$ symmetric, field theory with fermion matter coupled
to a topological Chern--Simons term, in the large $N$ limit is analyzed in
details. We determine the conditions for the existence of a massless conformal
invariant ground state as well as the conditions for a massive phase. We
analyze the phase structure and calculate gauge invariant corelators comparing
them in several cases to existing results. In addition to the non-critical
explicitly broken scale invariance massive case we consider also a massive
ground state where the scale symmetry is spontaneously broken. We show that
such a phase appears only in the presence of a marginal deformation that is
introduced by adding a certain scalar auxiliary field and discuss the
fermion-boson dual mapping. The ground state contains in this case a massless
$U(N)$ singlet bound state goldstone boson- the dilaton whose properties are
determined. We employ here the temporal gauge which is at variance with respect
to past calculations using the light-cone gauge and thus, a check (though
limited) of gauge independence is at hand. The large $N$ properties are
determined by using a field integral formalism and the steepest descent method.
The saddle point equations, which take here the form of integral equations for
non-local fields, determine the mass gap and the dressed fermion propagator.
Vertex functions are calculated at leading order in $1/N$ as exact solutions of
integral equations. From the vertex functions, we infer gauge invariant
two-point correlation functions for scalar operators and a current. Indications
about the consistency of the method are obtained by verifying that
gauge-invariant quantities have a natural $O(3)$ covariant form. As a further
verification, in several occasions, a few terms of the perturbative expansion
are calculated and compared with the exact results in the appropriate order.
