Related papers: Universal critical behavior in tensor models for f…
We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to…
A unified theory of four-dimensional gravity together with the standard model is presented, with supersymmetry breaking of M-theory at a TeV. Masses of the the known particles are derived. The cosmological constant is quantum generated to…
We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the…
Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic…
We investigate the finite-size scaling of the boundary quantum geometric tensor (QGT) numerically close to the Anderson localization transition in the presence of small external magnetic fields. The QGT exhibits universal scaling and…
We consider a dynamical triangulation model of euclidean quantum gravity where the topology is not fixed. This model is equivalent to a tensor generalization of the matrix model of two dimensional quantum gravity. A set of moves is given…
We develop a generic spacetime model in General Relativity which can be used to build any gravitational model within General Relativity. The generic model uses two types of assumptions: (a) Geometric assumptions additional to the inherent…
A stochastic theory of gravity is described in which the metric tensor is a random variable such that the spacetime manifold is a fluctuating physical system at a certain length scale. A general formalism is described for calculating…
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…
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…
We study four-dimensional gravity theories that are rendered renormalisable by the inclusion of curvature-squared terms to the usual Einstein action with cosmological constant. By choosing the parameters appropriately, the massive scalar…
Combining asymptotically safe quantum gravity with a tensor field theory, we exhibit the first example of a theory with gravity and scalar fields in four dimensions which may realize asymptotic safety at a non-vanishing value of the scalar…
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…
Rooted in group field theory and matrix models, random tensor models are a recent background-invariant approach to quantum gravity in arbitrary dimensions. Colored tensor models (CTM) generate random triangulated orientable…
This thesis is driven by a central question: "What can we learn from random geometries about the structure of quantum spacetime?" In Chapter 2, we provide a partial review of the mathematical foundation of this thesis, random geometry. In…
We construct all the unitary cubic curvature gravity theories built on the contractions of the Riemann tensor in D -dimensional (anti)-de Sitter spacetimes. Our construction is based on finding the equivalent quadratic action for the…
One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
Geometric quantum computation offers a potential route to fault-tolerant quantum information processing by exploiting the global nature of geometric phases. However, achieving controlled high-order suppression of multiple error sources…
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…