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We study here a complete quantization of a Callan-Giddings-Harvey-Strominger(CGHS) vacuum model following loop quantum gravity techniques. Concretely, weadopt a formulation of the model in terms of a set of new variables thatresemble the ones commonly employed in spherically symmetric loop quantumgravity. The classical theory consists of two pairs of canonical variables plusa scalar and diffeomorphism (first class) constraints. We consider a suitableredefinition 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 thedilaton field. On the one hand, we find a suitable invariant domain of thescalar constraint operator, and we construct explicitly its solution space.There, the eigenvalues of the dilaton and the metric operators cannot vanishlocally, allowing us to conclude that singular geometries are ruled out in thequantum theory. On the other hand, the physical Hilbert space is constructedout of them, after group averaging the previous states with the diffeomorphismconstraint. In turn, we identify the standard observable corresponding to themass of the black hole at the boundary, in agreement with the classical theory.We also construct an additional observable on the bulk associated with thesquare of the dilaton field, with no direct classical analog.

Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution