Topological versus Non--Topological Theories and $p-q$ Duality in $c\le 1$ 2d Gravity Models

Abstract

We discuss the non--perturbative formulation for $c\le 1$ string theory. The field theory like formulation of topological and non--topological models is presented. The integral representation for arbitrary $(p,q)$ solutions is derived which explicitly obeys $p-q$ duality of these theories. The exact solutions to string equation and various examples are also discussed.

15 pp, preprint FIAN/TD-15/92, latex