Hausdorff dimension of fermions on a random lattice

TL;DR

This paper introduces a new computational method for simulating fermions coupled with lattice quantum gravity, specifically measuring the Hausdorff dimension of Majorana spinors on a random lattice, with results aligning with theoretical bounds.

Contribution

A novel simulation technique for gravity-fermion interactions on lattices, enabling the study of non-Riemannian models with precise Hausdorff dimension measurements.

Findings

Hausdorff dimension of fermions: 4.22 +/- 0.03

Method applicable to non-Riemannian gravity models

Results consistent with literature bounds

Abstract

Geometric properties of lattice quantum gravity in two dimensions are studied numerically via Monte Carlo on Euclidean Dynamical Triangulations. A new computational method is proposed to simulate gravity coupled with fermions, which allows the study of interacting theories on a lattice, such as non-Riemannian gravity models. This was tested on Majorana spinors, where we obtained a Hausdorff dimension dW = 4.22 +/- 0.03, consistent with the bounds from the literature 4.19 < dH < 4.21.