Geometry of the quantum universe

A universe much like the (Euclidean) de Sitter space-time appears as background geometry in the causal dynamical triangulation (CDT) regularization of quantum gravity. We study the geometry of such universes which appear in the path integral as a function of the bare coupling constants of the theory.Comment: 19 pages, 7 figures. Typos corrected. Conclusions unchange

On the Quantum Geometry of Multi-critical CDT

We discuss extensions of a recently introduced model of multi-critical CDT to higher multi-critical points. As in the case of pure CDT the continuum limit can be taken on the level of the action and the resulting continuum surface model is again described by a matrix model. The resolvent, a simple observable of the quantum geometry which is accessible from the matrix model is calculated for arbitrary multi-critical points. We go beyond the matrix model by determining the propagator using the peeling procedure which is used to extract the effective quantum Hamiltonian and the fractal dimension in agreement with earlier results by Ambjorn et al. With this at hand a string field theory formalism for multi-critical CDT is introduced and it is shown that the Dyson-Schwinger equations match the loop equations of the matrix model. We conclude by commenting on how to formally obtain the sum over topologies and a relation to stochastic quantisation.Comment: 15 pages, 2 figures, improved discussion, some new results regarding Hausdorff dimension, as publishe

A Lorentzian cure for Euclidean troubles

There is strong evidence coming from Lorentzian dynamical triangulations that the unboundedness of the gravitational action is no obstacle to the construction of a well-defined non-perturbative path integral. In a continuum approach, a similar suppression of the conformal divergence comes about as the result of a non-trivial path-integral measure.Comment: 3 page

The transfer matrix in four-dimensional CDT

The Causal Dynamical Triangulation model of quantum gravity (CDT) has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of the scale factor of the (CDT) universe are well described by an effective transfer matrix where the matrix elements are labeled only by the scale factor. Using computer simulations we determine the effective transfer matrix elements and show how they relate to an effective minisuperspace action at all scales.Comment: 32 pages, 19 figure

CDT meets Horava-Lifshitz gravity

The theory of causal dynamical triangulations (CDT) attempts to define a nonperturbative theory of quantum gravity as a sum over space-time geometries. One of the ingredients of the CDT framework is a global time foliation, which also plays a central role in the quantum gravity theory recently formulated by Ho\v{r}ava. We show that the phase diagram of CDT bears a striking resemblance with the generic Lifshitz phase diagram appealed to by Ho\v{r}ava. We argue that CDT might provide a unifying nonperturbative framework for anisotropic as well as isotropic theories of quantum gravity.Comment: 17 pages, 3 figures. Typos corrected, a few remarks added

A new perspective on matter coupling in 2d quantum gravity

We provide compelling evidence that a previously introduced model of non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional) flat-space behaviour when coupled to Ising spins. The evidence comes from both a high-temperature expansion and from Monte Carlo simulations of the combined gravity-matter system. This weak-coupling behaviour lends further support to the conclusion that the Lorentzian model is a genuine alternative to Liouville quantum gravity in two dimensions, with a different, and much `smoother' critical behaviour.Comment: 24 pages, 7 figures (postscript

The Semiclassical Limit of Causal Dynamical Triangulations

Previous work has shown that the macroscopic structure of the theory of quantum gravity defined by causal dynamical triangulations (CDT) is compatible with that of a de Sitter universe. After emphasizing the strictly nonperturbative nature of this semiclassical limit we present a detailed study of the three-volume data, which allows us to re-confirm the de Sitter structure, exhibit short-distance discretization effects, and make a first detailed investigation of the presence of higher-order curvature terms in the effective action for the scale factor. Technically, we make use of a novel way of fixing the total four-volume in the simulations.Comment: 30 pages, 10 figure

The 3d Ising Model represented as Random Surfaces

We consider a random surface representation of the three-dimensional Ising model.The model exhibit scaling behaviour and a new critical index \k which relates \g_{string} for the bosonic string to the exponent \a of the specific heat of the 3d Ising model is introduced. We try to determine \k by numerical simulations.Comment: No figures included. Available by ordinary mail on request. 13 pages. Latex. preprint NBI-HE-92-8

Real--time dynamics of a hot Yang-Mills theory: a numerical analysis

We discuss recent results obtained from simulations of high temperature, classical, real time dynamics of SU(2) Yang-Mills theory at temperatures of the order of the electroweak scale. Measurements of gauge covariant and gauge invariant autocorrelations of the fields indicate that the ASY-Bodecker scenario is irrelevant at these temperatures.Comment: 3 pages, 3 figures, Lattice2001(hitemp

Nonperturbative Quantum Gravity

Asymptotic safety describes a scenario in which general relativity can be quantized as a conventional field theory, despite being nonrenormalizable when expanding it around a fixed background geometry. It is formulated in the framework of the Wilsonian renormalization group and relies crucially on the existence of an ultraviolet fixed point, for which evidence has been found using renormalization group equations in the continuum. "Causal Dynamical Triangulations" (CDT) is a concrete research program to obtain a nonperturbative quantum field theory of gravity via a lattice regularization, and represented as a sum over spacetime histories. In the Wilsonian spirit one can use this formulation to try to locate fixed points of the lattice theory and thereby provide independent, nonperturbative evidence for the existence of a UV fixed point. We describe the formalism of CDT, its phase diagram, possible fixed points and the "quantum geometries" which emerge in the different phases. We also argue that the formalism may be able to describe a more general class of Ho\v{r}ava-Lifshitz gravitational models.Comment: Review, 146 pages, many figure