6,037 research outputs found
Evidence for Asymptotic Safety from Lattice Quantum Gravity
We calculate the spectral dimension for nonperturbative quantum gravity
defined via Euclidean dynamical triangulations. We find that it runs from a
value of ~3/2 at short distance to ~4 at large distance scales, similar to
results from causal dynamical triangulations. We argue that the short distance
value of 3/2 for the spectral dimension may resolve the tension between
asymptotic safety and the holographic principle.Comment: 4 pages, 2 figures. Minor typos corrected, clarifications and
reference added. Conforms with version published in PR
Hypothesis on the Nature of Time
We present numerical evidence that fictitious diffusing particles in the
causal dynamical triangulation (CDT) approach to quantum gravity exceed the
speed of light on small distance scales. We argue this superluminal behaviour
is responsible for the appearance of dimensional reduction in the spectral
dimension. By axiomatically enforcing a scale invariant speed of light we show
that time must dilate as a function of relative scale, just as it does as a
function of relative velocity. By calculating the Hausdorff dimension of CDT
diffusion paths we present a seemingly equivalent dual description in terms of
a scale dependent Wick rotation of the metric. Such a modification to the
nature of time may also have relevance for other approaches to quantum gravity.Comment: 15 pages, 4 figures. Conforms with version to be published in PRD.
Clarifications and references adde
Exploring Euclidean Dynamical Triangulations with a Non-trivial Measure Term
We investigate a nonperturbative formulation of quantum gravity defined via
Euclidean dynamical triangulations (EDT) with a non-trivial measure term in the
path integral. We are motivated to revisit this older formulation of dynamical
triangulations by hints from renormalization group approaches that gravity may
be asymptotically safe and by the emergence of a semiclassical phase in causal
dynamical triangulations (CDT). We study the phase diagram of this model and
identify the two phases that are well known from previous work: the branched
polymer phase and the collapsed phase. We verify that the order of the phase
transition dividing the branched polymer phase from the collapsed phase is
almost certainly first-order. The nontrivial measure term enlarges the phase
diagram, allowing us to explore a region of the phase diagram that has been
dubbed the crinkled region. Although the collapsed and branched polymer phases
have been studied extensively in the literature, the crinkled region has not
received the same scrutiny. We find that the crinkled region is likely a part
of the collapsed phase with particularly large finite-size effects.
Intriguingly, the behavior of the spectral dimension in the crinkled region at
small volumes is similar to that of CDT, as first reported in arXiv:1104.5505,
but for sufficiently large volumes the crinkled region does not appear to have
4-dimensional semiclassical features. Thus, we find that the crinkled region of
the EDT formulation does not share the good features of the extended phase of
CDT, as we first suggested in arXiv:1104.5505. This agrees with the recent
results of arXiv:1307.2270, in which the authors used a somewhat different
discretization of EDT from the one presented here.Comment: 36 pages, 27 figures. Typos corrected, improved analysis of phase
transition, and clarifications added. Conclusions unchanged. Conforms with
version published in JHE
IPN localizations of Konus short gamma-ray bursts
Between the launch of the \textit{GGS Wind} spacecraft in 1994 November and
the end of 2010, the Konus-\textit{Wind} experiment detected 296 short-duration
gamma-ray bursts (including 23 bursts which can be classified as short bursts
with extended emission). During this period, the IPN consisted of up to eleven
spacecraft, and using triangulation, the localizations of 271 bursts were
obtained. We present the most comprehensive IPN localization data on these
events. The short burst detection rate, 18 per year, exceeds that of many
individual experiments.Comment: Published versio
Ideal triangulations of 3-manifolds up to decorated transit equivalences
We consider 3-dimensional pseudo-manifolds M with a given set of marked point
V such that M-V is the interior of a compact 3-manifold with boundary. An ideal
triangulation T of (M, V ) has V as its set of vertices. A branching (T, b)
enhances T to a Delta-complex. Branched triangulations of (M, V ) are
considered up to the b-transit equivalence generated by isotopy and ideal
branched moves which keep V pointwise fixed. We extend a well known
connectivity result for naked triangulations by showing that branched ideal
triangulations of (M, V) are equivalent to each other. A pre-branching is a
system of transverse orientations at the 2-facets of T verifying a certain
global constraint; pre-branchings are considered up to a natural pb-transit
equivalence. If M is oriented, every branching b induces a pre-branching w(b)
and every b-transit induces a pb-transit. The quotient set of pre-branchings up
to transit equivalence is far to be trivial; we get some information about it
and we characterize the pre-branchings of type w(b). Pre-branched and branched
moves are naturally organized in subfamilies which give rise to restricted
transit equivalences. In the branching setting we revisit early results about
the sliding transit equivalence and outline a conceptually different approach
to the branched connectivity and eventually also to the naked one. The basic
idea is to point out some structures of differential topological nature which
are carried by every branched ideal triangulation, are preserved by the sliding
transits and can be modified by the whole branched transits. The non ambiguous
transit equivalence already widely studied on pre-branchings lifts to a
specialization of the sliding equivalence on branchings; we point out a few
specific insights, again in terms of carried structures preserved by the non
ambiguous and which can be modified by the whole sliding transits.Comment: 29 pages, 22 figure
Singular Vertices and the Triangulation Space of the D-sphere
By a sequence of numerical experiments we demonstrate that generic
triangulations of the sphere for contain one {\it singular}
simplex. The mean number of elementary simplices sharing this
simplex increases with the volume of the triangulation according to a simple
power law. The lower dimension subsimplices associated with this
simplex also show a singular behaviour. Possible consequences for the
DT model of four-dimensional quantum gravity are discussed.Comment: 15 pages, 9 figure
Fixed versus random triangulations in 2D simplicial Regge calculus
We study 2D quantum gravity on spherical topologies using the Regge calculus
approach with the measure. Instead of a fixed non-regular triangulation
which has been used before, we study for each system size four different random
triangulations, which are obtained according to the standard Voronoi-Delaunay
procedure. We compare both approaches quantitatively and show that the
difference in the expectation value of between the fixed and the random
triangulation depends on the lattice size and the surface area . We also try
again to measure the string susceptibility exponents through a finite-size
scaling Ansatz in the expectation value of an added interaction term in
an approach where is held fixed. The string susceptibility exponent
is shown to agree with theoretical predictions for the sphere,
whereas the estimate for appears to be too negative.Comment: 4 latex pages + 4 ps-figs. + espcrc2.sty, poster presented by W.
Janke at LATTICE96(gravity
Geodesic distances in Liouville quantum gravity
In order to study the quantum geometry of random surfaces in Liouville
gravity, we propose a definition of geodesic distance associated to a Gaussian
free field on a regular lattice. This geodesic distance is used to numerically
determine the Hausdorff dimension associated to shortest cycles of 2d quantum
gravity on the torus coupled to conformal matter fields, showing agreement with
a conjectured formula by Y. Watabiki. Finally, the numerical tools are put to
test by quantitatively comparing the distribution of lengths of shortest cycles
to the corresponding distribution in large random triangulations.Comment: 21 pages, 8 figure
- …