Loop models, Marginally Rough Interfaces, and the Coulomb Gas

TL;DR

This paper develops a field theory for 2D loop models by mapping them to interface models, leading to exact critical exponents and conformal charge predictions based solely on geometry and conformal invariance.

Contribution

It introduces a novel coarse-graining approach that maps loop models to a Liouville field theory with imaginary couplings, providing exact critical data.

Findings

Exact critical exponents derived from the theory

Conformal charge of loop models determined

Physical interpretation of Dotsenko-Fateev screening charge

Abstract

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.