4,063 research outputs found
Counting a black hole in Lorentzian product triangulations
We take a step toward a nonperturbative gravitational path integral for
black-hole geometries by deriving an expression for the expansion rate of null
geodesic congruences in the approach of causal dynamical triangulations. We
propose to use the integrated expansion rate in building a quantum horizon
finder in the sum over spacetime geometries. It takes the form of a counting
formula for various types of discrete building blocks which differ in how they
focus and defocus light rays. In the course of the derivation, we introduce the
concept of a Lorentzian dynamical triangulation of product type, whose
applicability goes beyond that of describing black-hole configurations.Comment: 42 pages, 11 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
Monte Carlo simulations of 4d simplicial quantum gravity
Dynamical triangulations of four-dimensional Euclidean quantum gravity give
rise to an interesting, numerically accessible model of quantum gravity. We
give a simple introduction to the model and discuss two particularly important
issues. One is that contrary to recent claims there is strong analytical and
numerical evidence for the existence of an exponential bound that makes the
partition function well-defined. The other is that there may be an ambiguity in
the choice of the measure of the discrete model which could even lead to the
existence of different universality classes.Comment: 16 pages, LaTeX, epsf, 4 uuencoded figures; contribution to the JMP
special issue on "Quantum Geometry and Diffeomorphism-Invariant Quantum Field
Theory
The Tensor Track, III
We provide an informal up-to-date review of the tensor track approach to
quantum gravity. In a long introduction we describe in simple terms the
motivations for this approach. Then the many recent advances are summarized,
with emphasis on some points (Gromov-Hausdorff limit, Loop vertex expansion,
Osterwalder-Schrader positivity...) which, while important for the tensor track
program, are not detailed in the usual quantum gravity literature. We list open
questions in the conclusion and provide a rather extended bibliography.Comment: 53 pages, 6 figure
Critical behavior of colored tensor models in the large N limit
Colored tensor models have been recently shown to admit a large N expansion,
whose leading order encodes a sum over a class of colored triangulations of the
D-sphere. The present paper investigates in details this leading order. We show
that the relevant triangulations proliferate like a species of colored trees.
The leading order is therefore summable and exhibits a critical behavior,
independent of the dimension. A continuum limit is reached by tuning the
coupling constant to its critical value while inserting an infinite number of
pairs of D-simplices glued together in a specific way. We argue that the
dominant triangulations are branched polymers.Comment: 20 page
A discrete history of the Lorentzian path integral
In these lecture notes, I describe the motivation behind a recent formulation
of a non-perturbative gravitational path integral for Lorentzian (instead of
the usual Euclidean) space-times, and give a pedagogical introduction to its
main features. At the regularized, discrete level this approach solves the
problems of (i) having a well-defined Wick rotation, (ii) possessing a
coordinate-invariant cutoff, and (iii) leading to_convergent_ sums over
geometries. Although little is known as yet about the existence and nature of
an underlying continuum theory of quantum gravity in four dimensions, there are
already a number of beautiful results in d=2 and d=3 where continuum limits
have been found. They include an explicit example of the inequivalence of the
Euclidean and Lorentzian path integrals, a non-perturbative mechanism for the
cancellation of the conformal factor, and the discovery that causality can act
as an effective regulator of quantum geometry.Comment: 38 pages, 16 figures, typos corrected, some comments and references
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