  We study here a complete quantization of a Callan-Giddings-Harvey-Strominger
(CGHS) vacuum model following loop quantum gravity techniques. Concretely, we
adopt a formulation of the model in terms of a set of new variables that
resemble the ones commonly employed in spherically symmetric loop quantum
gravity. The classical theory consists of two pairs of canonical variables plus
a scalar and diffeomorphism (first class) constraints. We consider a suitable
redefinition of the Hamiltonian constraint such that the new constraint algebra
(with structure constants) is well adapted to the Dirac quantization approach.
For it, we adopt a polymeric representation for both the geometry and the
dilaton field. On the one hand, we find a suitable invariant domain of the
scalar constraint operator, and we construct explicitly its solution space.
There, the eigenvalues of the dilaton and the metric operators cannot vanish
locally, allowing us to conclude that singular geometries are ruled out in the
quantum theory. On the other hand, the physical Hilbert space is constructed
out of them, after group averaging the previous states with the diffeomorphism
constraint. In turn, we identify the standard observable corresponding to the
mass of the black hole at the boundary, in agreement with the classical theory.
We also construct an additional observable on the bulk associated with the
square of the dilaton field, with no direct classical analog.
