Quantization of coset space sigma-models coupled to two-dimensional gravity

TL;DR

This paper develops an exact quantization framework for two-dimensional coset space sigma-models coupled to gravity, connecting classical observables to quantum solutions via advanced mathematical structures.

Contribution

It extends previous work by formulating a two-time Hamiltonian approach and relating the model's quantum solutions to a modified Knizhnik-Zamolodchikov system.

Findings

Derived the complete phase space in the isomonodromic sector.

Quantized Dirac brackets and linked to Wheeler-DeWitt solutions.

Explored algebraic structure of quantum observables.

Abstract

The mathematical framework for an exact quantization of the two-dimensional coset space sigma-models coupled to dilaton gravity, that arise from dimensional reduction of gravity and supergravity theories, is presented. Extending previous results 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. On the classical level, a set of observables is identified, that is complete for essential sectors of the theory. Quantum counterparts of these observables and their algebraic structure are investigated. Their status in alternative quantization procedures is discussed, employing the link with Hamiltonian Chern-Simons theory.