  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. As a consequence, we prove that the Liouville field concentrates on
the solution of the classical Liouville equation with explicit negative scalar
curvature. We also characterize the leading fluctuations, which are Gaussian
and massive, and establish a large deviation principle. Though considered as an
ansatz in the whole physics literature, it seems that it is the first rigorous
probabilistic derivation of the semiclassical limit of LFT. On the other hand,
we carry out the same analysis when we further weight the Liouville action with
heavy matter operators. This procedure appears when computing the $n$-points
correlation functions of LFT.
