Semiclassical limit of Liouville Field Theory

Understand

Liouville Field Theory (LFT for short) is a two dimensional model of random surfaces, which is for instance involved in $2d$ string theory or in the description of the fluctuations of metrics in $2d$ Liouville quantum gravity.

• This is a probabilistic model that consists in weighting the classical Free Field action with an interaction term given by the exponential of a Gaussian multiplicative chaos.
• The main input of our work is the study of the semiclassical limit of the theory, which is a prescribed asymptotic regime of LFT of interest in physics literature (see \cite{witten} and references therein).
• We derive exact formulas for the Laplace transform of the Liouville field in the case of flat metric on the unit disk with Dirichlet boundary conditions.