2D QUANTUM-GRAVITY, TOPOLOGICAL FIELD-THEORY AND THE MULTICRITICAL MATRIX MODELS

We discuss the theory of 2D quantum gravity coupled to a c = -2 conformal field theory. We show that this theory has an interpretation as a topological field theory. The correlation functions of this theory are identical to those of the K = 1 multicritical matrix model, which is believed to be the discrete analogue of this continuum theory. We show that by perturbing the topological field theory, one can also recover the higher multicritical points, corresponding to the K > 1 matrix models. Finally, we introduce the N = 1 supersymmetric analogue of this topological field theory, 2D quantum supergravity coupled to a c ̂ = 1 superconformal field theory. The multicritical behaviour of this model will be discussed in a separate publication. © 1990.