ON 2D GRAVITY IN CONFORMAL FIELD-THEORY

2D quantum gravity may be investigated in the conventional formalism of conformal field theory (CFT). The main results of this approach are reviewed. Operators of vanishing dimension appear to play an important role in the topological sector of the theory. The value c=-2 seems distinguished in such a continual theory, just as it does in the lattice and topological approaches to 2D gravity. An attempt to find the CFT counterparts of the ghost operators, introduced in the topological approach, is described. This opens the possibility to check explicitly the interrelations between their correlators, evaluated by Witten. We suggest that these may be intimately related to the Euler characteristics of the relevant module spaces. © 1990.