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

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 $D_S=2$.

arXiv comment13 pages, 8 figures

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• The unitary conformal field theory behind 2D Asymptotic Safety
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Quantum Flatness in Two-Dimensional CDT Quantum Gravity
• Scalar fields in Causal Dynamical Triangulations
• The cylinder amplitude in the Hard Dimer model on 2D Causal Dynamical Triangulations
• The impact of a random metric upon a diffusing particle