Scale-dependent Hausdorff dimensions in 2d gravity

TL;DR

This paper investigates how different scaling of coupling constants in 2D gravity models creates a continuum of geometries with varying fractal properties, bridging causal and ordinary dynamical triangulations.

Contribution

It introduces a one-parameter family of 2D gravity ensembles that interpolate between causal and ordinary dynamical triangulations, analyzing their fractal dimensions.

Findings

Identifies global and local Hausdorff dimensions of the continuum geometries.

Establishes a connection between different triangulation ensembles via scaling.

Provides insights into the fractal nature of 2D quantum gravity models.

Abstract

By appropriate scaling of coupling constants a one-parameter family of ensembles of two-dimensional geometries is obtained, which interpolates between the ensembles of (generalized) causal dynamical triangulations and ordinary dynamical triangulations. We study the fractal properties of the associated continuum geometries and identify both global and local Hausdorff dimensions.