Related papers: Spectral Dimension from Nonlocal Dynamics on Causa…
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…
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…
We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the…
An important probe of quantum geometry is its spectral dimension, defined via a spatial diffusion process. In this work we study the spectral dimension of a ``spatial hypersurface'' in a manifoldlike causal set using the induced spatial…
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…
Within the causal dynamical triangulations approach to the quantization of gravity, striking evidence has emerged for the dynamical reduction of spacetime dimension on sufficiently small scales. Specifically, the spectral dimension…
In recent years several approaches to quantum gravity have found evidence for a scale dependent spectral dimension of space-time varying from four at large scales to two at small scales of order of the Planck length. The first evidence came…
The seemingly universal phenomenon of scale-dependent effective dimensions in non-perturbative theories of quantum gravity has been shown to be a potential source of quantum gravity phenomenology. The scale-dependent effective dimension…
We analyze the universal properties of a new two-dimensional quantum gravity model defined in terms of Locally Causal Dynamical Triangulations (LCDT). Measuring the Hausdorff and spectral dimensions of the dynamical geometrical ensemble, we…
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…
If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches…
The scalar modes of the geometry induced by dimensional decoupling are investigated. In the context of the low energy string effective action, solutions can be found where the spatial part of the background geometry is the direct product of…
Causal set non-local wave operators allow both for the definition of an action for Causal set theory and the study of deviations from local physics that may have interesting phenomenological consequences. It was previously shown that, in…
Hints from a number of different approaches to quantum gravity point to a phenomenon of "spontaneous dimensional reduction" to two spacetime dimensions near the Planck scale. I examine the physical meaning of the term "dimension" in this…
We derive general properties of the scale-dependent effective spectral dimensions of non-perturbative gauge boson propagators as they appear as solutions from different methods in Yang-Mills theories. In the ultraviolet and for short time…
A good generalization of the Euclidean dimension to disordered systems and non crystalline structures is commonly required to be related to large scale geometry and it is expected to be independent of local geometrical modifications. The…
We study the dispersive properties of a linear equation in one spatial dimension which is inspired by models in peridynamics. The interplay between nonlocality and dispersion is analyzed in detail through the study of the asymptotics at low…
We explore the ultraviolet continuum regime of causal dynamical triangulations, as probed by the flow of the spectral dimension. We set up a framework in which one can find continuum theories that can in principle fully reproduce the…
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…
Recently a definition for a Lorentz invariant operator approximating the d'Alembertian in d-dimensional causal set space-times has been proposed. This operator contains several dimension-dependent constants which have been determined for…