title: Three-Point Functions in c≤1 Liouville Theory and Conformal Loop Ensembles.
abstract: The possibility of extending the Liouville conformal field theory from values of the central charge c≥25 to c≤1 has been debated for many years in condensed matter physics as well as in string theory. It was only recently proven that such an extension-involving a real spectrum of critical exponents as well as an analytic continuation of the Dorn-Otto-Zamolodchikov-Zamolodchikov formula for three-point couplings-does give rise to a consistent theory. We show in this Letter that this theory can be interpreted in terms of microscopic loop models. We introduce in particular a family of geometrical operators, and, using an efficient algorithm to compute three-point functions from the lattice, we show that their operator algebra corresponds exactly to that of vertex operators V_{α[over ^]} in c≤1 Liouville theory. We interpret geometrically the limit α[over ^]→0 of V_{α[over ^]} and explain why it is not the identity operator (despite having conformal weight Δ=0).
authors.affiliation: Sorbonne Universités, UPMC Université Paris 6, UMR 7589, LPTHE, F-75005 Paris, France.|CNRS, UMR 7589, LPTHE, F-75005 Paris, France.
authors.forename: Yacine
authors.initials: Y
authors.lastname: Ikhlef
authors.affiliation: Laboratoire de Physique Théorique, École Normale Supérieure-PSL Research University, 24 rue Lhomond, F-75231 Paris Cedex 05, France.|Sorbonne Universités, UPMC Université Paris 6, CNRS UMR 8549, F-75005 Paris, France.|Institut de Physique Théorique, CEA Saclay, 91191 Gif Sur Yvette, France.
authors.forename: Jesper Lykke
authors.initials: JL
authors.lastname: Jacobsen
authors.affiliation: Institut de Physique Théorique, CEA Saclay, 91191 Gif Sur Yvette, France.|Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0484, USA.
authors.forename: Hubert
authors.initials: H
authors.lastname: Saleur