Related papers: Fractal Structure of Quantum Gravity in Two Dimens…
We answer to 72 frequently asked questions about theories of multifractional spacetimes. Apart from reviewing and reorganizing what we already know about such theories, we discuss the physical meaning and consequences of the very recent…
Assuming a fractal distribution of matter in the universe, consequences that follow from the General Theory of Relativity and the Copernican Principle for fractal cosmology are examined. The change in perspective necessary to deal with a…
Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the…
We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative…
In this paper we have calculated the spectral dimension of loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We have obtained that the spectral dimension of the spatial section runs…
Content: 1. Introduction 2. Regge calculus and dynamical triangulations Simplicial manifolds and piecewise linear spaces - dual complex and volume elements - curvature and Regge action - topological invariants - quantum Regge calculus -…
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…
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
Liouville quantum gravity (LQG) is a one-parameter family of models of random fractal surfaces which first appeared in the physics literature in the 1980s. Recent works have constructed a metric (distance function) on an LQG surface. We…
The two-dimensional theory of gravity describing a graviton-dilaton system is considered. The graviton-dilaton coupling can be fixed such that the quantum theory remains free of the conformal anomaly for any conformal dimension of the…
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…
The nonlinear structures in 2D quantum gravity coupled to the $(q+1,q)$ minimal model are studied in the Liouville theory to clarify the factorization and the physical states. It is confirmed that the dressed primary states outside the…
The study of the packing of a length of wire in a two dimensional domain is done using techniques of conformal maps. The resulting scaling properties are derived through the Coulomb gas formalism of Conformal Field Theories. An analogy is…
We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the…
Topological defects in the framework of effective quantum gravity model are investigated, based on the hypothesis of an effective fractal dimension of the universe. This is done by using Caputo fractional derivatives to determine the…
In an extension of speculations that physical space-time is a fractal which might itself be embedded in a high-dimensional continuum, it is hypothesized to "compensate" for local variations of the fractal dimension by instead varying the…
Within the path integral formalism, we compute the disk partition functions of two dimensional Liouville and JT quantum gravity theories coupled to a matter CFT of central charge $c$, with cosmological constant $\Lambda$, in the limit…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
We develop worldline formulations of covariant fracton gauge theories. These are a one-parameter family of gauge theories of a rank-two symmetric tensor field, invariant under a scalar gauge transformation involving a double derivative.…