A Universal Fractal Structure of 2D Quantum Gravity for c > 1

TL;DR

This paper explores the fractal structure of 2D quantum gravity coupled with matter fields, revealing a potential universal behavior for central charges greater than one, with implications for understanding quantum gravity's geometric properties.

Contribution

It proposes a possible universal fractal structure for 2D quantum gravity for c > 1, based on distributions of baby universes, extending previous understanding limited to c ≤ 1.

Findings

Distributions of baby universes are similar for different matter fields with the same c.

The data suggests a universal fractal structure for 1 < c ≤ 4.

String susceptibility $ = 1/3$ is compatible with the observed distributions.

Abstract

We investigate the fractal structure of $2d$ quantum gravity coupled to matter by measuring the distributions of so-called baby universes. We demonstrate that the method works well as long as $c \leq 1$. For $c >1$ it is not clear what distribution to expect. However, we observe strikingly similar distributions for various kinds of matter fields with the same $c$. This indicate that there might be some range of $c >1$ where the central charge of the matter fields alone determines the fractal structure of gravity coupled to matter. The hypothesis that the string susceptibility $\g = 1/3$ is found to be compatible with the data for $1 < c \leq 4$.