scholarly journals Searching for a continuum limit in causal dynamical triangulation quantum gravity

2016 ◽  
Vol 93 (10) ◽  
Author(s):  
J. Ambjorn ◽  
D. N. Coumbe ◽  
J. Gizbert-Studnicki ◽  
J. Jurkiewicz
Keyword(s):  
Quantum Gravity ◽  
Continuum Limit ◽  
Dynamical Triangulation

scholarly journals A toy model of discretized gravity in two dimensions and its extensions

2017 ◽  
Vol 32 (28) ◽  
pp. 1750149
Author(s):  
Marcello Rotondo ◽  
Shin’ichi Nojiri
Keyword(s):  
Quantum Gravity ◽  
Continuum Limit ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Expectation Value ◽  
Dynamical Triangulation ◽  
Physical Quantities ◽  
Euclidean Signature

We propose a toy model of quantum gravity in two dimensions with Euclidean signature. The model is given by a kind of discretization which is different from the dynamical triangulation. We show that there exists a continuum limit and we can calculate some physical quantities such as the expectation value of the area, that is, the volume of the two-dimensional Euclidean spacetime. We also consider the extensions of the model to higher dimensions.

Gravité quantique et modèles de matrices

1991 ◽  
Vol 69 (7) ◽  
pp. 837-854 ◽  
Author(s):  
David Sénéchal
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Gravity ◽  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Continuum Limit ◽  
Two Dimensional ◽  
Planar Approximation ◽  
Conformal Field ◽  
The Matrix

A review of the main results recently obtained in the study of two-dimensional quantum gravity is offered. The analysis of two-dimensional quantum gravity by the methods of conformal field theory is briefly described. Then the treatment of quantum gravity in terms of matrix models is explained, including the notions of continuum limit, planar approximation, and orthogonal polynomials. Correlation fonctions are also treated, as well as phases of the matrix models.

scholarly journals Status of Background-Independent Coarse Graining in Tensor Models for Quantum Gravity

Universe ◽  
2019 ◽  
Vol 5 (2) ◽  
pp. 53 ◽  
Author(s):  
Astrid Eichhorn ◽  
Tim Koslowski ◽  
Antonio Pereira
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Continuum Limit ◽  
Three Dimensional ◽  
Coarse Graining ◽  
Discrete Models ◽  
Practical Implementation ◽  
Tensor Model ◽  
Independent Form ◽  
Tensor Models

A background-independent route towards a universal continuum limit in discrete models of quantum gravity proceeds through a background-independent form of coarse graining. This review provides a pedagogical introduction to the conceptual ideas underlying the use of the number of degrees of freedom as a scale for a Renormalization Group flow. We focus on tensor models, for which we explain how the tensor size serves as the scale for a background-independent coarse-graining flow. This flow provides a new probe of a universal continuum limit in tensor models. We review the development and setup of this tool and summarize results in the two- and three-dimensional case. Moreover, we provide a step-by-step guide to the practical implementation of these ideas and tools by deriving the flow of couplings in a rank-4-tensor model. We discuss the phenomenon of dimensional reduction in these models and find tentative first hints for an interacting fixed point with potential relevance for the continuum limit in four-dimensional quantum gravity.

scholarly journals THE WEINGARTEN MODEL À LA POLYAKOV

1992 ◽  
Vol 07 (18) ◽  
pp. 1651-1660 ◽  
Author(s):  
SIMON DALLEY
Keyword(s):  
Quantum Gravity ◽  
Matrix Models ◽  
Critical Behavior ◽  
Continuum Limit ◽  
Hermitian Matrix ◽  
Gauge Model ◽  
Vertex Models ◽  
Lattice Gauge ◽  
Genus Expansion ◽  
The Continuum

The Weingarten lattice gauge model of Nambu-Goto strings is generalized to allow for fluctuations of an intrinsic worldsheet metric through a dynamical quadrilation. The continuum limit is taken for c≤1 matter, reproducing the results of Hermitian matrix models to all orders in the genus expansion. For the compact c=1 case the vortices are Wilson lines, whose exclusion leads to the theory of non-interacting fermions. As a by-product of the analysis one finds the critical behavior of SOS and vertex models coupled to 2D quantum gravity.

SIMULATIONS OF FOUR-DIMENSIONAL SIMPLICIAL QUANTUM GRAVITY AS DYNAMICAL TRIANGULATION

1992 ◽  
Vol 07 (12) ◽  
pp. 1039-1061 ◽  
Author(s):  
M.E. AGISHTEIN ◽  
A.A. MIGDAL
Keyword(s):  
Phase Transition ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Order Phase Transition ◽  
Transition Point ◽  
Second Order ◽  
Closed Universe ◽  
Statistical Limit ◽  
Dynamical Triangulation ◽  
Second Order Phase Transition

Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. We studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: we reached about 5×104 simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model should be further adjusted to reach the second order phase transition point, where the correlation length grows to infinity. We varied the gravitational constant, and we found the first order phase transition, similar to the one found in three-dimensional model, except in 4D the fluctuations are rather large at the transition point, so that this is close to the second order phase transition. The average curvature in cutoff units is large and positive in one phase (gravity), and small negative in another (antigravity). We studied the fractal geometry of both phases, using the heavy particle propagator to define the geodesic map, as well as with the old approach using the shortest lattice paths. The heavy propagator geodesic appeared to be much smoother, so that the scaling laws were found, corresponding to finite fractal dimensions: D+~2.3 in the gravity phase and D−~4.6 in the antigravity phase. Similar, but somewhat lower numbers were obtained from the heat kernel singularity. The influence of the αR2 terms in 2, 3 and 4 dimensions is discussed.

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