851 research outputs found
Wilson Fermions on a Randomly Triangulated Manifold
A general method of constructing the Dirac operator for a randomly
triangulated manifold is proposed. The fermion field and the spin connection
live, respectively, on the nodes and on the links of the corresponding dual
graph. The construction is carried out explicitly in 2-d, on an arbitrary
orientable manifold without boundary. It can be easily converted into a
computer code. The equivalence, on a sphere, of Majorana fermions and Ising
spins in 2-d is rederived. The method can, in principle, be extended to higher
dimensions.Comment: 18 pages, latex, 6 eps figures, fig2 corrected, Comment added in the
conclusion sectio
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.Comment: To appear in "Handbook of Spacetime", Springer Verlag. 31 page
Perturbing General Uncorrelated Networks
This paper is a direct continuation of an earlier work, where we studied
Erd\"os-R\'enyi random graphs perturbed by an interaction Hamiltonian favouring
the formation of short cycles. Here, we generalize these results. We keep the
same interaction Hamiltonian but let it act on general graphs with uncorrelated
nodes and an arbitrary given degree distribution. It is shown that the results
obtained for Erd\"os-R\'enyi graphs are generic, at the qualitative level.
However, scale-free graphs are an exception to this general rule and exhibit a
singular behaviour, studied thoroughly in this paper, both analytically and
numerically.Comment: 7 pages, 7 eps figures, 2-column revtex format, references adde
CDT---an Entropic Theory of Quantum Gravity
In these lectures we describe how a theory of quantum gravity may be
constructed in terms of a lattice formulation based on so-called causal
dynamical triangulations (CDT). We discuss how the continuum limit can be
obtained and how to define and measure diffeomorphism-invariant correlators. In
four dimensions, which has our main interest, the lattice theory has an
infrared limit which can be identified with de Sitter spacetime. We explain why
this infrared property of the quantum spacetime is nontrivial and due to
"entropic" effects encoded in the nonperturbative path integral measure. This
makes the appearance of the de Sitter universe an example of true emergence of
classicality from microscopic quantum laws. We also discuss nontrivial aspects
of the UV behaviour, and show how to investigate quantum fluctuations around
the emergent background geometry. Finally, we consider the connection to the
asymptotic safety scenario, and derive from it a new, conjectured scaling
relation in CDT quantum gravity.Comment: 49 pages, many figures. Lectures presented at the "School on
Non-Perturbative Methods in Quantum Field Theory" and the "Workshop on
Continuum and Lattice Approaches to Quantum Gravity", Sussex, September
15th-19th 2008 . To appear as a contribution to a Springer Lecture Notes in
Physics boo
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.Comment: Typos corrected, 21 page
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.Comment: 14 pages,lot of figure
Wilson loops in CDT quantum gravity
By explicit construction, we show that one can in a simple way introduce and
measure gravitational holonomies and Wilson loops in lattice formulations of
nonperturbative quantum gravity based on (Causal) Dynamical Triangulations. We
use this set-up to investigate a class of Wilson line observables associated
with the world line of a point particle coupled to quantum gravity, and deduce
from their expectation values that the underlying holonomies cover the group
manifold of SO(4) uniforml
Branched Polymers with Loops
We propose a classification of critical behaviours of branched polymers for arbitrary topology. We show that in an appropriately defined double scaling limit the singular part of the partition function is universal. We calculate this partition function exactly in the generic case and perturbatively otherwise. In the discussion section we comment on the relation between branched polymer theory and Euclidean quantum gravity
- …