a U(1) Kac-Moody Model Coupled to 2D-GRAVITY

We consider a simple model of a scalar field with U(1) Kac-Moody local symmetry coupled to 2D-gravity in order to clarify the origin of Stuckelberg symmetry in the w∞-gravity theory. An analogous symmetry takes place in our model too. The possible central extension of the complete symmetry algebra and the corresponding critical dimension have been found. The analysis of the Hamiltonian and the constraints shows that the generators of the Kac-Moody, the reparametrization and the Stuckelberg symmetries are not independent. The connection of the model with w1+∞- and W1+∞-gravity is discussed.