Hausdorff dimension of fermions on a random lattice

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 dH=4.22±0.04, consistent with the bounds from the literature 4.19<dH<4.21.