1,503 research outputs found
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
Shaken, but not stirred - Potts model coupled to quantum gravity
We investigate the critical behaviour of both matter and geometry of the
three-state Potts model coupled to two-dimensional Lorentzian quantum gravity
in the framework of causal dynamical triangulations. Contrary to what general
arguments of the effects of disorder suggest, we find strong numerical evidence
that the critical exponents of the matter are not changed under the influence
of quantum fluctuations in the geometry, compared to their values on fixed,
regular lattices. This lends further support to previous findings that quantum
gravity models based on causal dynamical triangulations are in many ways better
behaved than their Euclidean counterparts.Comment: 19 pages, 9 figure
Baby Universes Revisited
The behaviour of baby universes has been an important ingredient in
understanding and quantifying non-critical string theory or, equivalently,
models of two-dimensional Euclidean quantum gravity coupled to matter. Within a
regularized description based on dynamical triangulations, we amend an earlier
conjecture by Jain and Mathur on the scaling behaviour of genus- surfaces
containing particular baby universe `necks', and perform a nontrivial numerical
check on our improved conjecture.Comment: 10 pages, 1 figur
The emergence of background geometry from quantum fluctuations
We show how the quantization of two-dimensional gravity leads to an
(Euclidean) quantum space-time where the average geometry is that of constant
negative curvature and where the Hartle-Hawking boundary condition arises
naturally.Comment: 12 page
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
A new continuum limit of matrix models
We define a new scaling limit of matrix models which can be related to the
method of causal dynamical triangulations (CDT) used when investigating
two-dimensional quantum gravity. Surprisingly, the new scaling limit of the
matrix models is also a matrix model, thus explaining why the recently
developed CDT continuum string field theory (arXiv:0802.0719) has a
matrix-model representation (arXiv:0804.0252).Comment: 17 pages, 2 figure
The nature of ZZ branes
In minimal non-critical string theory we show that the principal (r,s) ZZ
brane can be viewed as the basic (1,1) ZZ boundary state tensored with the
(r,s) Cardy boundary state. In this sense there exists only one ZZ boundary
state, the basic (1,1) boundary state.Comment: 10 pages, footnote adde
Gauge fixing in Causal Dynamical Triangulations
We relax the definition of the Ambjorn-Loll causal dynamical triangulation
model in 1+1 dimensions to allow for a varying lapse. We show that, as long as
the spatially averaged lapse is constant in time, the physical observables are
unchanged in the continuum limit. This supports the claim that the time slicing
of the model is the result of a gauge fixing, rather than a physical preferred
time slicing.Comment: 14 pages, 2 figure
On subdivision invariant actions for random surfaces
We consider a subdivision invariant action for dynamically triangulated
random surfaces that was recently proposed (R.V. Ambartzumian et. al., Phys.
Lett. B 275 (1992) 99) and show that it is unphysical: The grand canonical
partition function is infinite for all values of the coupling constants. We
conjecture that adding the area action to the action of Ambartzumian et. al.
leads to a well-behaved theory.Comment: 7 pages, Latex, RH-08-92 and YITP/U-92-3
An Analytical Analysis of CDT Coupled to Dimer-like Matter
We consider a model of restricted dimers coupled to two-dimensional causal
dynamical triangulations (CDT), where the dimer configurations are restricted
in the sense that they do not include dimers in regions of high curvature. It
is shown how the model can be solved analytically using bijections with
decorated trees. At a negative critical value for the dimer fugacity the model
undergoes a phase transition at which the critical exponent associated to the
geometry changes. This represents the first account of an analytical study of a
matter model with two-dimensional interactions coupled to CDT.Comment: 12 pages, many figures, shortened, as publishe
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