Search for Scaling Dimensions for Random Surfaces with c=1

TL;DR

This paper numerically investigates the fractal geometry of random surfaces coupled with matter fields of central charge c=1, confirming the theoretical prediction of the intrinsic Hausdorff dimension using advanced simulation techniques.

Contribution

It provides the first large-scale numerical simulation of c=1 random surfaces, validating the theoretical Hausdorff dimension prediction with new computational methods.

Findings

Results agree with the theoretical $d_H = 2+\sqrt{2}$ prediction

Simulated surfaces contained up to 260,000 triangles

Used baby universe surgery for efficient simulation

Abstract

We study numerically the fractal structure of the intrinsic geometry of random surfaces coupled to matter fields with $c=1$. Using baby universe surgery it was possible to simulate randomly triangulated surfaces made of 260.000 triangles. Our results are consistent with the theoretical prediction $d_H = 2+\sqrt{2}$ for the intrinsic Hausdorff dimension.