  We consider a system of 2D interacting fermions with a flat Fermi surface.
The apparent conflict between Luttinger and non Luttinger liquid behavior found
through different approximations is resolved by showing the existence of a line
of non trivial fixed points, for the RG flow, corresponding to Luttinger liquid
behavior; the presence of marginally relevant operators can cause flow away
from the fixed point. The analysis is non-perturbative and based on the
implementation, at each RG iteration, of Ward Identities obtained from local
phase transformations depending on the Fermi surface side, implying the partial
vanishing of the Beta function.
