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Liouville Field Theory and Log-Correlated Random Energy Models.
Physical Review Letters 2017 March 4
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.
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