Finite size scaling in 2d causal set quantum gravity

Glaser, Lisa; O’Connor, Denjoe; Surya, Sumati

doi:10.1088/1361-6382/aa9540

Cited by 31 publications

(79 citation statements)

References 25 publications

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“…It was recently demonstrated by Glaser et al (2018) using finite size scaling arguments that that this is a first order phase transition. The analysis moreover suggests that the continuum phase corresponds to a spacetime with negative cosmological constant.…”

Section: A Continuum-inspired Dynamicsmentioning

confidence: 99%

“…We can then use standard tools in statistical physics, including 29 We leave out interpretational questions! MCMC methods, to find the expectation values of suitable observables (Surya 2012;Glaser and Surya 2016;Glaser et al 2018;Glaser 2018). In Henson et al (2017), MCMC methods were used to examine the sample space of naturally labelled posetsΩ n to determine the onset of the KR regime, using the uniform measure (β = 0).…”

Section: A Continuum-inspired Dynamicsmentioning

confidence: 99%

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The causal set approach to quantum gravity

2019

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The causal set theory (CST) approach to quantum gravity postulates that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or "causal sets". The partial order on a causal set represents a proto-causality relation while local finiteness encodes an intrinsic discreteness. In the continuum approximation the former corresponds to the spacetime causality relation and the latter to a fundamental spacetime atomicity, so that finite volume regions in the continuum contain only a finite number of causal set elements. CST is deeply rooted in the Lorentzian character of spacetime, where a primary role is played by the causal structure poset. Importantly, the assumption of a fundamental discreteness in CST does not violate local Lorentz invariance in the continuum approximation. On the other hand, the combination of discreteness and Lorentz invariance gives rise to a characteristic non-locality which distinguishes CST from most other approaches to quantum gravity.In this review we give a broad, semi-pedagogical introduction to CST, highlighting key results as well as some of the key open questions. This review is intended both for the beginner student in quantum gravity as well as more seasoned researchers in the field.

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Section: A Continuum-inspired Dynamicsmentioning

confidence: 99%

Section: A Continuum-inspired Dynamicsmentioning

confidence: 99%

The causal set approach to quantum gravity

2019

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“…Finally, as in all related work [19,22,23], there is the question of the analytic continuation and the physical significance of β in full Lorentzian quantum gravity. This remains an important open question.…”

Section: Discussionmentioning

confidence: 94%

“…We have also restricted our analysis here to fixed values of n, without addressing the question of how robust the results are in the asymptotic or large n limit. As shown in [23] using a finite sized scaling analysis for the 2d orders, one must look for scaling behaviour with β, n and . Work is currently being done towards this goal [30].…”

Section: Discussionmentioning

confidence: 99%

Dimensionally restricted causal set quantum gravity: examples in two and three dimensions

Cunningham

Surya

2020

Class. Quantum Grav.

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We study dimensionally restricted non-perturbative causal set quantum dynamics in 2 and 3 spacetime dimensions with non-trivial global spatial topology. The causal set sample space is generated from causal embeddings into latticisations of flat background spacetimes with global spatial topology S 1 and T 2 in 2 and 3 dimensions, respectively. The quantum gravity partition function over these sample spaces is studied using Markov Chain Monte Carlo (MCMC) simulations via an analytic continuation of a parameter β analogous to an inverse temperature. In both 2 and 3 dimensions we find a phase transition that separates the dominance of the action from that of the entropy. The action dominated phase is characterised by "layered" posets with a high degree of connectivity, while the causal sets in the entropy dominated phase are manifold-like. These results are similar in character to those obtained for topologically trivial causal set dynamics over the sample space of 2-orders. The current simulations use a newly developed framework for causal set MCMC calculations, and provide the first implementation of a 3 dimensional causal set dynamics.

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“…In causal set quantum gravity, the quantisation proceeds via the path-integral formalism. A candidate dynamics, the Benincasa-Dowker action [25][26][27] provides a starting point to evaluate the path integral via Monte Carlo simulations [40][41][42]. In this paper, we will not consider the path integral over all causal sets.…”

Section: Spatial Diffusion On a Causal Setmentioning

confidence: 99%

Spectral dimension on spatial hypersurfaces in causal set quantum gravity

Eichhorn

Surya

Versteegen

2019

Class. Quantum Grav.

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An important probe of quantum geometry is its spectral dimension, defined via a spatial diffusion process. In this work we study the spectral dimension of a "spatial hypersurface" in a manifoldlike causal set using the induced spatial distance function. In previous work, the diffusion was taken on the full causal set, where the nearest neighbours are unbounded in number. The resulting superdiffusion leads to an increase in the spectral dimension at short diffusion times, in contrast to other approaches to quantum gravity. In the current work, by using a temporal localisation in the causal set, the number of nearest spatial neighbours is rendered finite. Using numerical simulations of causal sets obtained from d = 3 Minkowski spacetime, we find that for a flat spatial hypersurface, the spectral dimension agrees with the Hausdorff dimension at intermediate scales, but shows clear indications of dimensional reduction at small scales, i.e., in the ultraviolet. The latter is a direct consequence of "discrete asymptotic silence" at small scales in causal sets. * eichhorn@sdu.dk

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Finite size scaling in 2d causal set quantum gravity

Cited by 31 publications

References 25 publications

The causal set approach to quantum gravity

The causal set approach to quantum gravity

Dimensionally restricted causal set quantum gravity: examples in two and three dimensions

Spectral dimension on spatial hypersurfaces in causal set quantum gravity

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