58 research outputs found

    Observables in Extended Percolation Models of Causal Set Cosmology

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    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

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    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

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    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 LL in such a way that they give a finite contribution in the LL \to \infty limit.Comment: Note adde

    Causal Set Topology

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    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

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    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

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    We study the NN-dependent behaviour of 2d\mathrm{2d} causal set quantum gravity. This theory is known to exhibit a phase transition as the analytic continuation parameter β\beta, akin to an inverse temperature, is varied. Using a scaling analysis we find that the asymptotic regime is reached at relatively small values of NN. Focussing on the 2d\mathrm{2d} causal set action SS, we find that βS\beta \langle S\rangle scales like Nν N^\nu where the scaling exponent ν\nu takes different values on either side of the phase transition. For β>βc\beta > \beta_c we find that ν=2\nu=2 which is consistent with our analytic predictions for a non-continuum phase in the large β\beta regime. For β<βc\beta<\beta_c we find that ν=0\nu=0, 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 2d\mathrm{2d} causal set quantum gravity for N65N \gtrsim 65.Comment: 32 pages, 27 figures (v2 typos and missing reference fixed
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