The spectral dimension in 2D CDT gravity coupled to scalar fields

TL;DR

This paper investigates the spectral dimension of two-dimensional Causal Dynamical Triangulations (CDT) with and without scalar fields, finding it remains consistent with a value of 2 regardless of matter content.

Contribution

It provides the first analysis of the spectral dimension in 2D CDT coupled to scalar fields, extending previous work on geometric properties of the model.

Findings

Spectral dimension remains approximately 2 for both pure gravity and with four scalar fields.

Presence of scalar fields does not alter the spectral dimension from the pure gravity case.

Results support the robustness of the spectral dimension as a geometric indicator in 2D CDT.

Abstract

Causal Dynamical Triangulations (CDT) provide a non-perturbative formulation of Quantum Gravity assuming the existence of a global time foliation. In our earlier study we analyzed the effect of including $d$ copies of a massless scalar field in the two-dimensional CDT model with imaginary time. For $d > 1$ we observed the formation of a "blob", somewhat similar to that observed in four-dimensional CDT without matter. In the two-dimensional case the "blob" has a Hausdorff dimension $D_H=3$. In this paper we study the spectral dimension $D_S$ of the two-dimensional CDT-universe, both for $d = 0$ (pure gravity) and $d = 4$. We show that in both cases the spectral dimension is consistent with $D_S = 2$.