Random Surfaces: A Non-Perturbative Regularization of Strings?

Abstract

I review the basic properties of the theory of random surfaces. While it is by now well known that the theory of (discretized) random surfaces correctly decribes the (perturbative) aspects of non-critical strings in d < 1 and 2D-gravity coupled to matter with central charge c < 1, not much is known about the non-critical strings for d > 1. In these lectures I intend to show that the theory of dynamical triangulated random surfaces provides us with a lot of information about the dynamics of both the bosonic string and the superstring even for d > 1. I also briefly review recent attempts to define a string field theory (sum over all genus) in this approach.