A Unitary S-matrix for 2D Black Hole Formation and Evaporation

We study the black hole information paradox in the context of a two-dimensional toy model given by dilaton gravity coupled toN massless scalar fields. After making the model well-defined by imposing reflecting boundary conditions at a critical value of the dilaton field, we quantize the theory and derive the quantum S-matrix for the case that N=24. This S-matrix is unitary by construction, and we further argue that in the semiclassical regime it describes the formation and subsequent Hawking evaporation of two-dimensional black holes. Finally, we note an interesting correspondence between the dilaton gravity S-matrix and that of the c = 1 matrix model.