Liouville field theory and log-correlated Random Energy Models

TL;DR

This paper establishes an exact connection between Liouville field theory and log-correlated Random Energy Models, revealing universal behaviors and providing precise numerical validation of the theoretical predictions.

Contribution

It introduces a novel exact mapping between Liouville field theory and log-correlated Random Energy Models, combining conformal bootstrap and replica symmetry breaking techniques.

Findings

Exact distribution of the energy landscape minimum obtained.

Universal behaviors in log-correlated Random Energy class unveiled.

High precision numerical tests confirm theoretical predictions.

Abstract

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.