Related papers: Spectral dimension on spatial hypersurfaces in cau…
We evaluate the spectral dimension in causal set quantum gravity by simulating random walks on causal sets. In contrast to other approaches to quantum gravity, we find an increasing spectral dimension at small scales. This observation can…
In this paper, we calculate in a transparent way the spectral dimension of a quantum spacetime, considering a diffusion process propagating on a fluctuating manifold. To describe the erratic path of the diffusion, we implement a minimal…
The so-called spectral dimension is a scale-dependent number associated with both geometries and field theories that has recently attracted much attention, driven largely though not exclusively by investigations of causal dynamical…
We explore the idea of asymptotic silence in causal set theory and find that causal sets approximated by continuum spacetimes exhibit behaviour akin to asymptotic silence. We make use of an intrinsic definition of spatial distance between…
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…
Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the…
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a)…
We extend the definition of "spectral dimension" (usually defined for fractal and lattice geometries) to theories on smooth spacetimes with anisotropic scaling. We show that in quantum gravity dominated by a Lifshitz point with dynamical…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Different approaches to quantum gravity generally predict that the dimension of spacetime at the fundamental level is not 4. The principal tool to measure how the dimension changes between the IR and UV scales of the theory is the spectral…
Results from a number of different approaches to quantum gravity suggest that the effective dimension of spacetime may drop to $d=2$ at small scales. I show that two different dimensional estimators in causal set theory display the same…
We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from…
This paper describes an approach that uses flat-spacetime dimension estimators to estimate the manifold dimension of causal sets that can be faithfully embedded into curved spacetimes. The approach is invariant under coarse graining and can…
We investigate the behavior of small subsets of causal sets that approximate Minkowski space in three, four, and five dimensions, and show that their effective dimension decreases smoothly at small distances. The details of the short…
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth…
Studies of the effective regime of loop quantum gravity (LQG) revealed that, in the limit of Planckian curvature scales, spacetime may undergo a transition from the Lorentzian to Euclidean signature. This effect is a consequence of quantum…
In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension $d$ at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is…
The phenomenon of scale dependent spectral dimension has attracted special interest in the quantum gravity community over the last eight years. It was first observed in computer simulations of the causal dynamical triangulation (CDT)…
Any discrete approach to quantum gravity must provide some prescription as to how to deduce continuum properties from the discrete substructure. In the causal set approach it is straightforward to deduce timelike distances, but surprisingly…
We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional…