  We develop a coarse-graining procedure for two-dimensional models of
fluctuating loops by mapping them to interface models. The result is an
effective field theory for the scaling limit of loop models, which is found to
be a Liouville theory with imaginary couplings. This field theory is {\it
completely specified} by geometry and conformal invariance {\it alone}, and it
leads to exact results for the critical exponents and the conformal charge of
loop models. A physical interpretation of the Dotsenko-Fateev screening charge
is found.
