Information is not lost in the evaporation of 2D black holes.

We analyze Hawking evaporation of the Callan-Giddings-Harvey-Strominger black holes from a quantum geometry perspective and show that information is not lost, primarily because the quantum space-time is sufficiently larger than the classical. Using suitable approximations to extract physics from quantum space-times we establish that (i) the future null infinity of the quantum space-time is sufficiently long for the past vacuum to evolve to a pure state in the future, (ii) this state has a finite norm in the future Fock space, and (iii) all the information comes out at future infinity; there are no remnants.