58 research outputs found
Observables in Extended Percolation Models of Causal Set Cosmology
Classical sequential growth models for causal sets provide an important step
towards the formulation of a quantum causal set dynamics. The covariant
observables in a class of these models known as generalised percolation have
been completely characterised in terms of physically well-defined ``stem sets''
and yield an insight into the nature of observables in quantum causal set
cosmology. We discuss a recent extension of generalised percolation and show
that the characterisation of covariant observables in terms of stem sets is
also complete in this extension.Comment: 14 pages, 2 figure
Towards a Definition of Locality in a Manifoldlike Causal Set
It is a common misconception that spacetime discreteness necessarily implies
a violation of local Lorentz invariance. In fact, in the causal set approach to
quantum gravity, Lorentz invariance follows from the specific implementation of
the discreteness hypothesis. However, this comes at the cost of locality. In
particular, it is difficult to define a "local" region in a manifoldlike causal
set, i.e., one that corresponds to an approximately flat spacetime region.
Following up on suggestions from previous work, we bridge this lacuna by
proposing a definition of locality based on the abundance of m-element
order-intervals as a function of m in a causal set. We obtain analytic
expressions for the expectation value of this function for an ensemble of
causal set that faithfully embeds into an Alexandrov interval in d-dimensional
Minkowski spacetime and use it to define local regions in a manifoldlike causal
set. We use this to argue that evidence of local regions is a necessary
condition for manifoldlikeness in a causal set. This in addition provides a new
continuum dimension estimator. We perform extensive simulations which support
our claims.Comment: 35 pages, 17 figure
On the Moduli Space of the Localized 1-5 System
We calculate the effective action for small velocity scattering of localized
1-branes and 5-branes. Momentum is allowed to flow in the direction along the
1-branes so that the moduli space has only 1/8 of the full supersymmetry.
Relative to the more familiar case with the 1-branes delocalized along the
5-branes, this introduces new moduli associated with the motion of the 1-branes
along the 5-branes. We consider in detail the moduli space metric for the
associated two body problem. Even for motion transverse to the 5-brane, our
results differ substantially from the delocalized case. However, this
difference only appears when both the 1-brane charge and the momentum charge
are localized. Despite the fact that, in a certain sense, 1-branes
spontaneously delocalize near a 5-brane horizon, the moduli space metric in
this limit continues to differ from the delocalized result. This fact may be of
use in developing a new description of the associated BPS bound states. The new
terms depend on the torus size in such a way that they give a finite
contribution in the limit.Comment: Note adde
Causal Set Topology
The Causal Set Theory (CST) approach to quantum gravity is motivated by the
observation that, associated with any causal spacetime (M,g) is a poset (M,<),
with the order relation < corresponding to the spacetime causal relation.
Spacetime in CST is assumed to have a fundamental atomicity or discreteness,
and is replaced by a locally finite poset, the causal set. In order to obtain a
well defined continuum approximation, the causal set must possess the requisite
intrinsic topological and geometric properties that characterise a continuum
spacetime in the large. The continuum approximation thus sets the stage for the
study of topology in CST. We review the status of causal set topology and
present some new results relating poset and spacetime topologies. The hope is
that in the process, some of the ideas and questions arising from CST will be
made accessible to the larger community of computer scientists and
mathematicians working on posets.Comment: Typos fixed, references updated. Latex 22 pages, 3 figure
The Discrete Geometry of a Small Causal Diamond
We study the discrete causal set geometry of a small causal diamond in a
curved spacetime using the average abundance of k-element chains or total
orders in the underlying causal set C. We begin by obtaining the first order
curvature corrections to the flat spacetime expression for the abundance using
Riemann normal coordinates. For fixed spacetime dimension this allows us to
find a new expression for the discrete scalar curvature of C as well as the
time-time component of its Ricci tensor in terms of the abundances of k-chains.
We also find a new dimension estimator for C which replaces the flat spacetime
Myrheim-Meyer estimator in generic curved spacetimes.Comment: 22 pages, 2 figure
Finite Size Scaling in 2d Causal Set Quantum Gravity
We study the -dependent behaviour of causal set quantum
gravity. This theory is known to exhibit a phase transition as the analytic
continuation parameter , akin to an inverse temperature, is varied.
Using a scaling analysis we find that the asymptotic regime is reached at
relatively small values of . Focussing on the causal set
action , we find that scales like where
the scaling exponent takes different values on either side of the phase
transition. For we find that which is consistent with
our analytic predictions for a non-continuum phase in the large regime.
For we find that , consistent with a continuum phase of
constant negative curvature thus suggesting a dynamically generated
cosmological constant. Moreover, we find strong evidence that the phase
transition is first order. Our results strongly suggest that the asymptotic
regime is reached in causal set quantum gravity for .Comment: 32 pages, 27 figures (v2 typos and missing reference fixed
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