Spacetime structures from critical values in two-dimensional quantum gravity

A model for two-dimensional (2D) quantum gravity is constructed out of the Virasoro group. To this end the quantization of the abstract Virasoro group is revisited. For the critical values of the conformal anomaly c, some quantum operators (SL(2, R) generators) lose their dynamical content (they are no longer conjugated operators). The notion of spacetime itself in 2D gravity then arises as associated with this kinematical SL(2, R) symmetry. An ensemble of different copies of AdS do co-exist in this model with different weights, depending on-their curvature (which is proportional to (h) over bar(2)) and they are connected by gravity operators. This model suggests that, in general, quantum diffeomorphisms should not be imposed as constraints to the theory, except for the classical limit.