title: Liouville Field Theory and Log-Correlated Random Energy Models.
abstract: An exact mapping is established between the c≥25 Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian free field plus a logarithmic confining potential. The probability distribution of the position of the minimum of the energy landscape is obtained exactly by combining the conformal bootstrap and one-step replica symmetry-breaking methods. Operator product expansions in the LFT allow us to unveil novel universal behaviors of the log-correlated random energy class. High-precision numerical tests are given.
authors.affiliation: LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
authors.forename: Xiangyu
authors.initials: X
authors.lastname: Cao
authors.affiliation: LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
authors.forename: Alberto
authors.initials: A
authors.lastname: Rosso
authors.affiliation: LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
authors.forename: Raoul
authors.initials: R
authors.lastname: Santachiara
authors.affiliation: CNRS-Laboratoire de Physique Théorique de l'École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex, France.
authors.forename: Pierre
authors.initials: P
authors.lastname: Le Doussal