Quantization of Coset Space σ-Models Coupled to Two-Dimensional Gravity

The mathematical framework for an exact quantization of the two-dimensio‐nal coset space σ-models coupled to dilaton gravity, that arise from dimensional reduction of gravity and supergravity theories, is presented. Extending previous results [49] the two-time Hamiltonian formulation is obtained, which describes the complete phase space of the model in the isomonodromic sector. The Dirac brackets arising from the coset constraints are calculated. Their quantization allows to relate exact solutions of the corresponding Wheeler–DeWitt equations to solutions of a modified (Coset-)Knizhnik-Zamolodchikov system.