923 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
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
On the Quantum Geometry of Multi-critical CDT
We discuss extensions of a recently introduced model of multi-critical CDT to
higher multi-critical points. As in the case of pure CDT the continuum limit
can be taken on the level of the action and the resulting continuum surface
model is again described by a matrix model. The resolvent, a simple observable
of the quantum geometry which is accessible from the matrix model is calculated
for arbitrary multi-critical points. We go beyond the matrix model by
determining the propagator using the peeling procedure which is used to extract
the effective quantum Hamiltonian and the fractal dimension in agreement with
earlier results by Ambjorn et al. With this at hand a string field theory
formalism for multi-critical CDT is introduced and it is shown that the
Dyson-Schwinger equations match the loop equations of the matrix model. We
conclude by commenting on how to formally obtain the sum over topologies and a
relation to stochastic quantisation.Comment: 15 pages, 2 figures, improved discussion, some new results regarding
Hausdorff dimension, as publishe
Crossing the c=1 barrier in 2d Lorentzian quantum gravity
In an extension of earlier work we investigate the behaviour of
two-dimensional Lorentzian quantum gravity under coupling to a conformal field
theory with c>1. This is done by analyzing numerically a system of eight Ising
models (corresponding to c=4) coupled to dynamically triangulated Lorentzian
geometries. It is known that a single Ising model couples weakly to Lorentzian
quantum gravity, in the sense that the Hausdorff dimension of the ensemble of
two-geometries is two (as in pure Lorentzian quantum gravity) and the matter
behaviour is governed by the Onsager exponents. By increasing the amount of
matter to 8 Ising models, we find that the geometry of the combined system has
undergone a phase transition. The new phase is characterized by an anomalous
scaling of spatial length relative to proper time at large distances, and as a
consequence the Hausdorff dimension is now three. In spite of this qualitative
change in the geometric sector, and a very strong interaction between matter
and geometry, the critical exponents of the Ising model retain their Onsager
values. This provides evidence for the conjecture that the KPZ values of the
critical exponents in 2d Euclidean quantum gravity are entirely due to the
presence of baby universes. Lastly, we summarize the lessons learned so far
from 2d Lorentzian quantum gravity.Comment: 21 pages, 18 figures (postscript), uses JHEP.cls, see
http://www.nbi.dk/~ambjorn/lqg2 for related animated simulation
RG flow in an exactly solvable model with fluctuating geometry
A recently proposed renormalization group technique, based on the
hierarchical structures present in theories with fluctuating geometry, is
implemented in the model of branched polymers. The renormalization group
equations can be solved analytically, and the flow in coupling constant space
can be determined.Comment: References updated, typos corrected and abstract sligtly changed. 10
pages. Pictex use
Causal random geometry from stochastic quantization
In this short note we review a recently found formulation of two-dimensional
causal quantum gravity defined through Causal Dynamical Triangulations and
stochastic quantization. This procedure enables one to extract the
nonperturbative quantum Hamiltonian of the random surface model including the
sum over topologies. Interestingly, the generally fictitious stochastic time
corresponds to proper time on the geometries.Comment: 5 pages, 2 figures, presented at XI Latin American Workshop on
Nonlinear Phenomena, Buzios, 2009, accepted for publication in Journal of
Physics: Conference Proceeding
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
The transfer matrix in four-dimensional CDT
The Causal Dynamical Triangulation model of quantum gravity (CDT) has a
transfer matrix, relating spatial geometries at adjacent (discrete lattice)
times. The transfer matrix uniquely determines the theory. We show that the
measurements of the scale factor of the (CDT) universe are well described by an
effective transfer matrix where the matrix elements are labeled only by the
scale factor. Using computer simulations we determine the effective transfer
matrix elements and show how they relate to an effective minisuperspace action
at all scales.Comment: 32 pages, 19 figure
On the relation between Euclidean and Lorentzian 2D quantum gravity
Starting from 2D Euclidean quantum gravity, we show that one recovers 2D
Lorentzian quantum gravity by removing all baby universes. Using a peeling
procedure to decompose the discrete, triangulated geometries along a
one-dimensional path, we explicitly associate with each Euclidean space-time a
(generalized) Lorentzian space-time. This motivates a map between the parameter
spaces of the two theories, under which their propagators get identified. In
two dimensions, Lorentzian quantum gravity can therefore be viewed as a
``renormalized'' version of Euclidean quantum gravity.Comment: 12 pages, 2 figure
A non-perturbative Lorentzian path integral for gravity
A well-defined regularized path integral for Lorentzian quantum gravity in
three and four dimensions is constructed, given in terms of a sum over
dynamically triangulated causal space-times. Each Lorentzian geometry and its
associated action have a unique Wick rotation to the Euclidean sector. All
space-time histories possess a distinguished notion of a discrete proper time.
For finite lattice volume, the associated transfer matrix is self-adjoint and
bounded. The reflection positivity of the model ensures the existence of a
well-defined Hamiltonian. The degenerate geometric phases found previously in
dynamically triangulated Euclidean gravity are not present. The phase structure
of the new Lorentzian quantum gravity model can be readily investigated by both
analytic and numerical methods.Comment: 11 pages, LaTeX, improved discussion of reflection positivity,
conclusions unchanged, references update
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