World-Sheet Geometry and Baby Universes in 2-D Quantum Gravity

Abstract

We show that the surface roughness for $c<1$ matter theories coupled to $2D$ quantum gravity is described by a self-similar structure of baby universes. There exist baby universes whose neck thickness is of the order of the ultraviolet cutoff, the largest of these having a macroscopic area $\sim A^{\frac{1}{1-\gamma }}$, where $A$ is the total area and $\gamma$ the string susceptibility exponent.

13 pages