820 research outputs found
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
Foliations and 2+1 Causal Dynamical Triangulation Models
The original models of causal dynamical triangulations construct space-time
by arranging a set of simplices in layers separated by a fixed time-like
distance. The importance of the foliation structure in the 2+1 dimensional
model is studied by considering variations in which this property is relaxed.
It turns out that the fixed-lapse condition can be equivalently replaced by a
set of global constraints that have geometrical interpretation. On the other
hand, the introduction of new types of simplices that puncture the foliating
sheets in general leads to different low-energy behavior compared to the
original model.Comment: v2: 9 pages, 3 figures, published versio
The phase structure of Causal Dynamical Triangulations with toroidal spatial topology
We investigate the impact of topology on the phase structure of
four-dimensional Causal Dynamical Triangulations (CDT). Using numerical Monte
Carlo simulations we study CDT with toroidal spatial topology. We confirm
existence of all four distinct phases of quantum geometry earlier observed in
CDT with spherical spatial topology. We plot the toroidal CDT phase diagram and
find that it looks very similar to the case of the spherical spatial topology.Comment: 24 pages, 15 figure
Quantum Gravity and Matter: Counting Graphs on Causal Dynamical Triangulations
An outstanding challenge for models of non-perturbative quantum gravity is
the consistent formulation and quantitative evaluation of physical phenomena in
a regime where geometry and matter are strongly coupled. After developing
appropriate technical tools, one is interested in measuring and classifying how
the quantum fluctuations of geometry alter the behaviour of matter, compared
with that on a fixed background geometry.
In the simplified context of two dimensions, we show how a method invented to
analyze the critical behaviour of spin systems on flat lattices can be adapted
to the fluctuating ensemble of curved spacetimes underlying the Causal
Dynamical Triangulations (CDT) approach to quantum gravity. We develop a
systematic counting of embedded graphs to evaluate the thermodynamic functions
of the gravity-matter models in a high- and low-temperature expansion. For the
case of the Ising model, we compute the series expansions for the magnetic
susceptibility on CDT lattices and their duals up to orders 6 and 12, and
analyze them by ratio method, Dlog Pad\'e and differential approximants. Apart
from providing evidence for a simplification of the model's analytic structure
due to the dynamical nature of the geometry, the technique introduced can shed
further light on criteria \`a la Harris and Luck for the influence of random
geometry on the critical properties of matter systems.Comment: 40 pages, 15 figures, 13 table
Quantum Gravity from Causal Dynamical Triangulations: A Review
This topical review gives a comprehensive overview and assessment of recent
results in Causal Dynamical Triangulations (CDT), a modern formulation of
lattice gravity, whose aim is to obtain a theory of quantum gravity
nonperturbatively from a scaling limit of the lattice-regularized theory. In
this manifestly diffeomorphism-invariant approach one has direct, computational
access to a Planckian spacetime regime, which is explored with the help of
invariant quantum observables. During the last few years, there have been
numerous new and important developments and insights concerning the theory's
phase structure, the roles of time, causality, diffeomorphisms and global
topology, the application of renormalization group methods and new observables.
We will focus on these new results, primarily in four spacetime dimensions, and
discuss some of their geometric and physical implications.Comment: 64 pages, 28 figure
The Universe from Scratch
A fascinating and deep question about nature is what one would see if one
could probe space and time at smaller and smaller distances. Already the
19th-century founders of modern geometry contemplated the possibility that a
piece of empty space that looks completely smooth and structureless to the
naked eye might have an intricate microstructure at a much smaller scale. Our
vastly increased understanding of the physical world acquired during the 20th
century has made this a certainty. The laws of quantum theory tell us that
looking at spacetime at ever smaller scales requires ever larger energies, and,
according to Einstein's theory of general relativity, this will alter spacetime
itself: it will acquire structure in the form of "curvature". What we still
lack is a definitive Theory of Quantum Gravity to give us a detailed and
quantitative description of the highly curved and quantum-fluctuating geometry
of spacetime at this so-called Planck scale. - This article outlines a
particular approach to constructing such a theory, that of Causal Dynamical
Triangulations, and its achievements so far in deriving from first principles
why spacetime is what it is, from the tiniest realms of the quantum to the
large-scale structure of the universe.Comment: 31 pages, 5 figures; review paper commissioned by Contemporary
Physics and aimed at a wider physics audience; minor beautifications,
coincides with journal versio
- …