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

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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 Dₕ=3. In this paper we study the spectral dimension Dₛ 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 Dₛ = 2.