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

TL;DR

This paper explores the geometric structure of 2D quantum gravity coupled with matter, revealing that surface roughness is characterized by a self-similar pattern of baby universes with specific size and area properties.

Contribution

It introduces a new description of surface roughness in 2D quantum gravity using baby universes and their self-similar structure for $c<1$ matter theories.

Findings

Baby universes exhibit a self-similar structure.

Largest baby universes have macroscopic area proportional to $A^{1/(1-\gamma)}$.

Surface roughness is linked to the distribution of baby universes.

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 $\sim A^{1 \over {1-\gamma}}$, where $A$ is the total area and $\gamma$ the string susceptibility exponent.