Exploring the Phase Diagram for Lattice Quantum Gravity

Coumbe, Daniel; Laiho, Jack

doi:10.22323/1.139.0334

Cited by 3 publications

(2 citation statements)

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“…Our studies show continuous behavior at this line, which is indicative of an analytic cross-over. Within the crinkled region finite-size effects are much greater than they are for β=0, and this previously led us to think that this phase possessed a 4-dimensional extended geometry [27,29,28]. However, simulations at larger volumes suggest that the crinkled region is a region within the collapsed phase with very large finite-size effects and long auto-correlation lengths.…”

Section: Overviewmentioning

confidence: 99%

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Exploring Euclidean dynamical triangulations with a non-trivial measure term

Coumbe

Laiho

2015

J. High Energ. Phys.

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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 finitesize 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.

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Section: Overviewmentioning

confidence: 99%

“…The parameter ∆ enlarges the phase diagram, and increasing ∆ away from zero permits the existence of the de Sitter phase. Thus, we investigate the result of including a third parameter in the bare lattice action of EDT [27,28,29]. In this work we add a local measure term to the calculation.…”

Section: Introductionmentioning

confidence: 99%

Exploring Euclidean dynamical triangulations with a non-trivial measure term

Coumbe

Laiho

2015

J. High Energ. Phys.

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Quantum Gravity via Causal Dynamical Triangulations

Ambjørn¹,

Görlich²,

Jurkiewicz

et al. 2014

Springer Handbooks

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Abstract"Causal Dynamical Triangulations" (CDT) represent a lattice regularization of the sum over spacetime histories, providing us with a non-perturbative formulation of quantum gravity. The ultraviolet fixed points of the lattice theory can be used to define a continuum quantum field theory, potentially making contact with quantum gravity defined via asymptotic safety. We describe the formalism of CDT, its phase diagram, and the quantum geometries emerging from it. We also argue that the formalism should be able to describe a more general class of quantum-gravitational models of Hořava-Lifshitz type.

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