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J. Ambjorn

Publications and source records attributed to J. Ambjorn.

At least 37 records · Page 2Linked to original sources
arXiv2015

The microscopic structure of 2D CDT coupled to matter

We show that for 1+1 dimensional Causal Dynamical Triangulations (CDT) coupled to 4 massive scalar fields one can construct an effective transfer matrix if the masses squared is larger than or equal to 0.05. The properties of this transfer matrix can explain why CDT coupled to matter can behave completely different from "pure" CDT. We identify the important critical exponent in the effective action, which may determine the universality class of the model.

gr-qc↗
arXiv2014

A restricted dimer model on a 2-dimensional random causal triangulation

We introduce a restricted hard dimer model on a random causal triangulation that is exactly solvable and generalizes a model recently proposed by Atkin and Zohren. We show that the latter model exhibits unusual behaviour at its multicritical point; in particular, its Hausdorff dimension equals 3 and not 3/2 as would be expected from general scaling arguments. When viewed as a special case of the generalized model introduced here we show that this behaviour is not generic and therefore is not likely to represent the true behaviour of the full dimer model on a random causal triangulation.

hep-th↗
arXiv2014

Renormalization Group Flow in CDT

We perform a first investigation of the coupling constant flow of the nonperturbative lattice model of four-dimensional quantum gravity given in terms of Causal Dynamical Triangulations (CDT). After explaining how standard concepts of lattice field theory can be adapted to the case of this background-independent theory, we define a notion of "lines of constant physics" in coupling constant space in terms of certain semiclassical properties of the dynamically generated quantum universe. Determining flow lines with the help of Monte Carlo simulations, we find that the second-order phase transition line present in this theory can be interpreted as a UV phase transition line if we allow for an anisotropic scaling of space and time.

hep-th↗
arXiv2014

A matrix model for strings beyond the c=1 barrier: the spin-s Heisenberg model on random surfaces

We consider a spin-s Heisenberg model coupled to two-dimensional quantum gravity. We quantize the model using the Feynman path integral, summing over all possible two-dimensional geometries and spin configurations. We regularize this path integral by starting with the R-matrices defining the spin-s Heisenberg model on a regular 2d Manhattan lattice. 2d quantum gravity is included by defining the R-matrices on random Manhattan lattices and summing over these, in the same way as one sums over 2d geometries using random triangulations in non-critical string theory. We formulate a random matrix model where the partition function reproduces the annealed average of the spin-s Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.

hep-th↗
arXiv2014

Scale-dependent Hausdorff dimensions in 2d gravity

By appropriate scaling of coupling constants a one-parameter family of ensembles of two-dimensional geometries is obtained, which interpolates between the ensembles of (generalized) causal dynamical triangulations and ordinary dynamical triangulations. We study the fractal properties of the associated continuum geometries and identify both global and local Hausdorff dimensions.

hep-th↗
arXiv2014

Effective QCD string beyond Nambu-Goto

We consider the QCD string as an effective string, whose action describes long-range stringy fluctuations. The leading infrared contribution to the ground state energy is given by the Alvarez-Arvis formula, usually derived using the Nambu-Goto action. Here we rederive it by a saddle point calculation using the Polyakov formulation of the free string, where the world sheet metric and the target space coordinates are treated as independent variables. The next order relevant in the infrared term in the effective action is the extrinsic curvature term. We show that the spectrum does not change order by order in the inverse string length, but may change at intermediate distances.

hep-th↗
arXiv2013

Two-Dimensional Quantum Geometry

In these lectures we review our present understanding of the fractal structure of two-dimensional Euclidean quantum gravity coupled to matter.

hep-th↗
arXiv2013

Euclidian 4d quantum gravity with a non-trivial measure term

We explore an extended coupling constant space of 4d regularized Euclidean quantum gravity, defined via the formalism of dynamical triangulations. We add a measure term which can also serve as a generalized higher curvature term and determine the phase diagram and the geometries dominating in the various regions. A first order phase transition line is observed, but no second order transition point is located. As a consequence we cannot attribute any continuum physics interpretation to the so-called crinkled phase of 4d dynamical triangulations.

hep-lat↗
arXiv2013

CDT and the Search for a Theory of Quantum Gravity

Causal Dynamical Triangulations provide a non-perturbative regularization of a theory of quantum gravity. We describe how this approach connects with the asymptotic safety program and Ho\vrava-Lifshitz gravity theory, and present the most recent results from computer simulations.

gr-qc↗
arXiv2013

2d CDT with gauge fields

Two-dimensional Causal Dynamical Triangulations provides a definition of the path integral for projectable two-dimensional Horava-Lifshitz quantum gravity. We solve the theory coupled to gauge fields.

hep-th↗
arXiv2013

The XXZ Heisenberg model on random surfaces

We consider integrable models, or in general any model defined by an $R$-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.

hep-th↗
arXiv2013

Universality of 2d causal dynamical triangulations

The formalism of Causal Dynamical Triangulations (CDT) attempts to provide a non-perturbative regularization of quantum gravity, viewed as an ordinary quantum field theory. In two dimensions one can solve the lattice theory analytically and the continuum limit is universal, not depending on the details of the lattice regularization.

hep-th↗
arXiv2013

Quantum Spacetime, from a Practitioner's Point of View

We argue that theories of quantum gravity constructed with the help of (Causal) Dynamical Triangulations have given us the most informative, quantitative models to date of quantum spacetime. Most importantly, these are derived dynamically from nonperturbative and background-independent quantum theories of geometry. In the physically relevant case of four spacetime dimensions, the ansatz of Causal Dynamical Triangulations produces - from a fairly minimal set of quantum field-theoretic inputs - an emergent spacetime which macroscopically looks like a de Sitter universe, and on Planckian scales possesses unexpected quantum properties. Important in deriving these results are a regularized version of the theory, in which the quantum dynamics is well defined, can be studied with the help of numerical Monte Carlo methods and extrapolated to infinite lattice volumes.

hep-th↗
arXiv2013

The transfer matrix method in four-dimensional causal dynamical triangulations

The Causal Dynamical Triangulation model of quantum gravity (CDT) is a proposition to evaluate the path integral over space-time geometries using a lattice regularization with a discrete proper time and geometries realized as simplicial manifolds. The model admits a Wick rotation to imaginary time for each space-time configuration. Using computer simulations we determined the phase structure of the model and discovered that it predicts a de Sitter phase with a four-dimensional spherical semi-classical background geometry. The model 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 labelled 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.

hep-th↗
arXiv2013

Quantum Gravity via Causal Dynamical Triangulations

"Causal Dynamical Triangulations" (CDT) represent a lattice regularization of the sum over spacetime histories, providing us with a non-perturbative formulation of quantum gravity. The ultraviolet fixed points of the lattice theory can be used to define a continuum quantum field theory, potentially making contact with quantum gravity defined via asymptotic safety. We describe the formalism of CDT, its phase diagram, and the quantum geometries emerging from it. We also argue that the formalism should be able to describe a more general class of quantum-gravitational models of Horava-Lifshitz type.

hep-th↗
arXiv2012

Second- and First-Order Phase Transitions in CDT

Causal Dynamical Triangulations (CDT) is a proposal for a theory of quantum gravity, which implements a path-integral quantization of gravity as the continuum limit of a sum over piecewise flat spacetime geometries. We use Monte Carlo simulations to analyse the phase transition lines bordering the physically interesting de Sitter phase of the four-dimensional CDT model. Using a range of numerical criteria, we present strong evidence that the so-called A-C transition is first order, while the B-C transition is second order. The presence of a second-order transition may be related to an ultraviolet fixed point of quantum gravity and thus provide the key to probing physics at and possibly beyond the Planck scale.

hep-th↗
arXiv2012

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 Hořava-Lifshitz gravitational models.

hep-th↗