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• W2767807568 abstract "The spectral dimension measures the dimensionality of a space as witnessed by a diffusing random walker. Within the causal dynamical triangulations approach to the quantization of gravity, the spectral dimension exhibits novel scale-dependent dynamics: reducing towards a value near 2 on sufficiently small scales, matching closely the topological dimension on intermediate scales, and decaying in the presence of positive curvature on sufficiently large scales. I report the first comprehensive scaling analysis of the small-to-intermediate scale spectral dimension for the test case of the causal dynamical triangulations of 3-dimensional Einstein gravity. I find that the spectral dimension scales trivially with the diffusion constant. I find that the spectral dimension is completely finite in the infinite volume limit, and I argue that its maximal value is exactly consistent with the topological dimension of 3 in this limit. I find that the spectral dimension reduces further towards a value near 2 as this case's bare coupling approaches its phase transition, and I present evidence against the conjecture that the bare coupling simply sets the overall scale of the quantum geometry. On the basis of these findings, I advance a tentative physical explanation for the dynamical reduction of the spectral dimension observed within causal dynamical triangulations: branched polymeric quantum geometry on sufficiently small scales. My analyses should facilitate attempts to employ the spectral dimension as a physical observable with which to delineate renormalization group trajectories in the hope of taking a continuum limit of causal dynamical triangulations at a nontrivial ultraviolet fixed point." @default.
• W2767807568 created "2017-11-17" @default.
• W2767807568 creator A5088039764 @default.
• W2767807568 date "2018-04-10" @default.
• W2767807568 modified "2023-09-25" @default.
• W2767807568 title "Scaling analyses of the spectral dimension in 3-dimensional causal dynamical triangulations" @default.
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• W2767807568 doi "https://doi.org/10.1088/1361-6382/aab86e" @default.
• W2767807568 hasPublicationYear "2018" @default.
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