  In this paper we will consider the Almheiri-Polchinski model of the AdS$_2$
back reaction coupled with Liouville field, which is necessary for quantum
consistency. In this model, the Liouville field is determined classically by a
bulk conformal transformation. The boundary time is also reparametrized by this
transformation. It is shown that the on-shell action on the boundary for the
gravity sector is given by a bulk integral containing the Liouville field. This
integral stems from Weyl anomaly and is SL(2,R) invariant. A prescription is
given for computing correlation functions of the operators dual to massless
scalars. The generating function of the correlation functions of these
operators is given by a sum of matter action and the bulk integral containing
the Liouville field. The latter integral leads to extra contributions to
$n(\geq 6)$ point functions.
