QUANTIZATION OF COSET SPACE SIGMA-MODELS COUPLED TO 2-DIMENSIONAL GRAVITY

The mathematical framework for an exact quantization of the two-dimens ional coset space sigma-models coupled to dilaton gravity, that arise from dimensional reduction of gravity and supergravity theories, is pr esented. Extending previous results [49] the two-time Hamiltonian form ulation is obtained, which describes the complete phase space of the m odel 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 solut ions of a modified (Coset-)Knizhnik-Zamolodchikov system. On the class ical level, a set of observables is identified, that is complete for e ssential sectors of the theory. Quantum counterparts of these observab les and their algebraic structure are investigated. Their status in al ternative quantization procedures is discussed, employing the link wit h Hamiltonian Chern-Simons theory.