The spectral dimension in 2D CDT gravity coupled to scalar fields
  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 $D_S = 2$. 
Jan Ambj{\o}rn, Andrzej G\"orlich, Jerzy Jurkiewicz, Hongguang Zhang
gr-qc hep-lat hep-th