Related papers: 2D Quantum Gravity -Three States of Surfaces-
Two-dimensional quantum gravity has led to numerous curious results since it was developed in the 1980s. Following the method of the original works, we derive the effective action for the simplest modifications of the theory, when the…
We introduce simple generic models of surface dynamics in loop quantum gravity (LQG). A quantum surface is defined as a set of elementary patches of area glued together. We provide it with an extra structure of locality (nearest neighbors),…
Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…
We consider two issues in the DT model of quantum gravity. First, it is shown that the triangulation space for D>3 is dominated by triangulations containing a single singular (D-3)-simplex composed of vertices with divergent dual volumes.…
Recent results obtained within a non-perturbative approach to quantum gravity based on the method of four-dimensional Causal Dynamical Triangulations are described. The phase diagram of the model consists of three phases. In the physically…
Two dimensional quantum R$^2$-gravity and its phase structure are examined in the semiclassical approach and compared with the results of the numerical simulation. Three phases are succinctly characterized by the effective action. A…
Using numerical data coming from Monte Carlo simulations of four-dimensional Causal Dynamical Triangulations, we study how automated machine learning algorithms can be used to recognize transitions between different phases of quantum…
We show that the surface roughness for $c<1$ matter theories coupled to $2D$ quantum gravity is described by a self-similar structure of baby universes. There exist baby universes whose neck thickness is of the order of the ultraviolet…
We study an ensemble of branched polymers which are embedded on other branched polymers. This is a toy model which allows us to study explicitly the reaction of a statistical system on an underlying geometrical structure, a problem of…
The geometry of 4D simplicial quantum gravity with a U(1) gauge field is studied numerically. The phase diagram shows a continuous transition when gravity is coupled with a U(1) gauge field. At the critical point measurements of the…
2D quantum gravity is the idea that a set of discretized surfaces (called map, a graph on a surface), equipped with a graph measure, converges in the large size limit (large number of faces) to a conformal field theory (CFT), and in the…
We review recent developments in the understanding of the fractal properties of quantum spacetime of 2d gravity coupled to c>0 conformal matter. In particular we discuss bounds put by numerical simulations using dynamical triangulations on…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use…
We consider methods of interpolating between the crystalline and dynamically triangulated random surface models. We argue that actions based on the deviation from six of the coordination number at a site are inadequate and propose an…
We show that generic kinetic growth processes with surface relaxations can exhibit a new crumpled phase with short-range orientational order at dimensions $d<4$. A sufficiently strong spatially non-local part of the chemical potential…
In the dynamical triangulation model of 4D euclidean quantum gravity we measure two-point functions of the scalar curvature as a function of the geodesic distance. To get the correlations it turns out that we need to subtract a squared…
For understanding the origin of anisotropies in the cosmic microwave background, rules to construct a quantized universe is proposed based on the dynamical triangulation method of the simplicial quantum gravity. A $d$-dimensional universe…
We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…
The complex structure of a surface generated by the two-dimensional dynamical triangulation(DT) is determined by measuring the resistivity of the surface. It is found that surfaces coupled to matter fields have well-defined complex…