Liouville field theory and log-correlated Random Energy Models
  An exact mapping is established between the $c\geq25$ 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 LFT allow to unveil novel universal behaviours of the log-correlated Random Energy class. High precision numerical tests are given. 
Xiangyu Cao, Pierre Le Doussal, Alberto Rosso, Raoul Santachiara
cond-mat.stat-mech cond-mat.dis-nn hep-th math-ph math.MP