  Jackiw Teitelboim (JT) gravity has proven to be an excellent tool for
investigating aspects of quantum gravity and black hole physics. In recent
years, the study of JT gravity and its deformations has helped us learn about
the different contributions of geometries in the gravitational path integral,
the quantum gravity Hilbert space, the space-time factorization problem, the
role of averaging in holography, the black hole information paradox, and the
matrix models. All this motivates the exploration of the JT gravity in
different setups, with and without matter. Here, we consider JT gravity
conformally coupled to Liouville field theory and matter fields. This model
admits to be interpreted as a non-critical string theory on a linear dilaton
background with a tachyonic Liouville potential along a null direction. The
constant curvature constraint of JT gravity results in a neutralization of the
Liouville mode, which makes it possible to compute the four-point correlation
function of the theory analytically. Here we give the explicit derivation of
the four-point function and briefly comment on its properties, such as
monodromy invariance, crossing symmetry, factorization, and limits.
