Related papers: From Trees to Gravity
Contents: 1. Introduction 2. Bosonic propagators and random paths 3. Random surfaces and strings 4. Matrix models and two-dimensional quantum gravity 5. The mystery of $c > 1$ 6. Euclidean quantum gravity in $d > 2$ 7. Discussion
The correspondence between quantum mechanics and noncommutative geometry is illustrated in the context of the noncommutative ${\rm AdS}^2_{\theta}/{\rm CFT_1}$ duality where ${\rm CFT}_1$ is identified as conformal quantum mechanics. This…
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…
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 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…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
We review the approach to quantum gravity based on supersymmetry, strings, and holography. This includes a survey of black holes in higher-dimensions, supersymmetry and supergravity, as well as string theory, black hole microstates, and the…
We study the fundamental question of how likely it is that two randomly chosen trees are isomorphic to each other for different models of random trees. We show that the probability decays exponentially for rooted labeled trees as well as…
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 analyze the framework recently proposed by Oppenheim et al. to model relativistic quantum fields coupled to relativistic, classical, stochastic fields (in particular, as a model of quantum matter coupled to ``classical gravity'').…
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…
Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical…
We consider Hilbert's problem of the axioms of Physics at a qualitative or conceptual level. This issue is more pressing than ever as we seek to understand how both General Relativity and quantum theory could emerge from some deeper theory…
General Theory of Relativity and Quantum theory gives two different description of the same mother nature in the big and small scale respectively. Mathematical languages of these two theories are entirely different, one is geometric while…
We review (and extend) the analysis of general theories of all interactions (gravity included) where the mass scales are due to dimensional transmutation. Quantum consistency requires the presence of terms in the action with four…
The macroscopic dimensions of space should not be input but rather output of a general model for physics. Here, dimensionality arises from a recently discovered mathematical bifurcation: positive versus indefinite manifold pairings. It is…
These lectures present an elementary introduction to quantum gauge fields. The first aim is to show how, in the tree approximation, gauge invariance follows from covariance and unitarity. This leads to the standard construction of the…
It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…
The spectrum of primordial perturbations obtained by calculating the quantum gravitational corrections to the dynamics of scalar perturbations is compared with Planck 2013 and BICEP2/{\it Keck Array} public data. The quantum gravitational…
The attempt of extending to higher dimensions the matrix model formulation of two-dimensional quantum gravity leads to the consideration of higher rank tensor models. We discuss how these models relate to four dimensional quantum gravity…