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We develop a coarse-graining procedure for two-dimensional models offluctuating loops by mapping them to interface models. The result is aneffective field theory for the scaling limit of loop models, which is found tobe a Liouville theory with imaginary couplings. This field theory is {\itcompletely specified} by geometry and conformal invariance {\it alone}, and itleads to exact results for the critical exponents and the conformal charge ofloop models. A physical interpretation of the Dotsenko-Fateev screening chargeis found.Comment: LaTex, 7 pages, 1 PostScript figure; uses epsf.sty. To appear in the  proceedings of the symposium''Exactly soluable models in Statistical  Mechanics'', March 1996, Northeastern University, Bosto

Loop Models, Marginally Rough Interfaces, and the Coulomb Gas