Related papers: Setting the physical scale of dimensional reductio…

Planck-scale dynamical dimensional reduction is attracting more and more interest in the quantum-gravity literature since it seems to be a model independent effect. However different studies base their results on different concepts of…

We derive the cutoff length scale of the quadratic gravity in $d \geq 5$ dimensional spacetime by demanding that the quantum focusing conjecture for the smeared quantum expansion holds at the classical level. The cutoff scale has different…

Studying spacetimes with continuous symmetries by dimensional reduction to a lower dimensional spacetime is a well known technique in field theory and gravity. Recently, its use has been advocated in numerical relativity as an efficient…

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…

We calculate the spectral dimension for nonperturbative quantum gravity defined via Euclidean dynamical triangulations. We find that it runs from a value of ~3/2 at short distance to ~4 at large distance scales, similar to results from…

We introduce an ensemble of infinite causal triangulations, called the uniform infinite causal triangulation, and show that it is equivalent to an ensemble of infinite trees, the uniform infinite planar tree. It is proved that in both cases…

Causal Dynamical Triangulations is a non-perturbative quantum gravity model, defined with a lattice cut-off. The model can be viewed as defined with a proper time but with no reference to any three-dimensional spatial background geometry.…

I briefly review some scenarios for the role of the Planck length in quantum gravity. In particular, I examine the differences between the schemes in which quantum gravity is expected to introduce a maximum acceleration and the schemes in…

A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional. I review this evidence, starting with a discussion of the physical meaning…

The limitations of three-dimensional semi-classical gravity are explored in the context of a conformally invariant theory for a self-interacting scalar field. The analysis of the theory's scaling behaviour reveals that scalar-loop effects…

The original models of causal dynamical triangulations construct space-time by arranging a set of simplices in layers separated by a fixed time-like distance. The importance of the foliation structure in the 2+1 dimensional model is studied…

We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of…

Several lines of evidence suggest that quantum gravity at very short distances may behave effectively as a two-dimensional theory. I summarize these hints, and offer an additional argument based on the strong-coupling limit of the…

A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Numerical simulations have given very interesting results in the cases of two, three and four…

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…

Using an octonionic formalism, we introduce a new mechanism for reducing 10 spacetime dimensions to 4 without compactification. Applying this mechanism to the free, 10-dimensional, massless (momentum space) Dirac equation results in a…

The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…

We summarize and expand our investigations concerning the soft graviton effects on microscopic matter dynamics in de Sitter space. The physical couplings receive IR logarithmic corrections which are sensitive to the IR cut-off at the…

Generalized causal dynamical triangulations (generalized CDT) is a model of two-dimensional quantum gravity in which a limited number of spatial topology changes is allowed to occur. We solve the model at the discretized level using…

Quantum-gravity renders the space-time dimension to depend on the size of region; it monotonically increases with the size of region and asymptotically approaches four for large distances. This effect was discovered in numerical simulations…