Dirac quantization of gravity-Yang-Mills systems in 1+1 dimensions.

In two dimensions a large class of gravitational systems including, e.g., R2gravity can be quantized exactly also when coupled dynamically to a Yang-Mills theory. Some previous considerations on the quantization of pure gravity theories are improved and generalized. Vienna, January 1993 ∗e-mail: [email protected] 1. In recent years the study of two-dimensional exactly solvable field theories has attracted considerable interest. One of the areas of investigations is 2D Yang-Mills (YM) theory (on a cylinder in a Hamiltonian approach [1], [2], or on an arbitrary Riemann surface when evaluating the partition function [3]); other models of interest are gravitational ones such as the one for 2D black hole [4], the Jackiw-Teitelboim model [5], or the Katanaev-Volovich (KV) model [6]. The first main purpose of this letter is to show that the exact quantum integrability extends to the combined treatment of the YM theory and a large class of gravitational systems. The gravitational part of the action considered in this work will be