Euclidian 4d quantum gravity with a non-trivial measure term

Ambjørn, J.; Glaser, Lisa; Görlich, Andrzej; Jurkiewicz, J.

doi:10.1007/jhep10(2013)100

Cited by 48 publications

(65 citation statements)

References 55 publications

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“…The Hausdorff dimension of a branched polymer is expected to be 2, a result that is confirmed by our previous calculations [18]. The spectral dimension of the branched polymer phase is expected to be D S = 4/3, a result that has also been numerically confirmed [17,18]. Once again, the properties of this phase make it a poor candidate for recovering four-dimensional space-time.…”

Section: Phase Diagramsupporting

confidence: 56%

“…Early work that included a nontrivial local measure term with a new arbitrary coupling identified a region of the extended phase diagram with properties that appeared to be different from the previously identified phases [20,21]; this was dubbed the crinkled region. However, follow-up studies showed that the crinkled region did not have desirable features, like a dimension close to four, suggesting that the crinkled region was most likely a part of the collapsed phase with particularly large finite-size effects [17,18]. The presence of a cross-over rather than a genuine phase transition between the collapsed phase and the crinkled region further supported this conclusion.…”

Section: Introductionsupporting

confidence: 53%

“…Two recent studies of this phase diagram, including the non-trivial measure term, were carried out in Ref. [17] (for combinatorial triangulations) and in Ref. [18] (for degenerate triangulations); the two works are in good agreement on the qualitative features of the EDT phase diagram.…”

Section: Phase Diagrammentioning

confidence: 61%

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Lattice quantum gravity and asymptotic safety

et al. 2017

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We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we argue that the target symmetry is the general coordinate invariance of the theory. After introducing and fine-tuning a non-trivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3/2, a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue that the number of relevant couplings in the continuum theory is one, once symmetry breaking by the lattice regulator is accounted for. Such a theory is maximally predictive, with no adjustable parameters. The cosmological constant in Planck units is the only relevant parameter, which serves to set the lattice scale. The cosmological constant in Planck units is of order one in the ultra-violet and undergoes renormalization group running to small values in the infrared. If these findings hold up under further scrutiny, the lattice may provide a nonperturbative definition of a renormalizable quantum field theory of general relativity with no adjustable parameters and a cosmological constant that is naturally small in the infrared.

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Section: Phase Diagramsupporting

confidence: 56%

Section: Introductionsupporting

confidence: 53%

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Lattice quantum gravity and asymptotic safety

et al. 2017

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“…The DT formalism was extended to higher dimensional gravity [20][21][22][23][24][25][26][27], but there it was less successful [28,29]. It is not ruled out that the theory can provide us with a successful version of quantum gravity, but if so the formulation has to be more elaborate than the first models (see [30][31][32][33] for recent attempts). However, there is one modification of DT which seems to work in the sense that lattice theory might have a non-trivial continuum limit, the so-called Causal Dynamical Triangulations model (CDT).…”

Section: Introductionmentioning

confidence: 99%

Towards an UV fixed point in CDT gravity

Ambjørn

Gizbert-Studnicki

Görlich

et al. 2019

J. High Energ. Phys.

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CDT is an attempt to formulate a non-perturbative lattice theory of quantum gravity. We describe the phase diagram and analyse the phase transition between phase B and phase C (which is the analogue of the de Sitter phase observed for the spherical spatial topology). This transition is accessible to ordinary Monte Carlo simulations when the topology of space is toroidal. We find that the transition is most likely first order, but with unusual properties. The end points of the transition line are candidates for second order phase transition points where an UV continuum limit might exist.

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“…Moreover, a first step connecting the NGFP to the underlying conformal field theory appeared in [64], possible completions of the flow at low energy have been discussed in [17,24,38,40,41] and geometric arguments determining the scaling of Newton's constant at the NGFP have been forwarded in [65,66]. In parallel Monte Carlo approaches to quantum gravity including Causal Dynamical Triangulations [67][68][69][70][71][72][73][74][75], Euclidean Dynamical Triangulations [76][77][78][79][80] and Lattice Quantum Gravity [81,82] made vast progress towards constructing phase diagrams at the non-perturbative level. While it is conceivable that all of these approaches probe the same universal short distance physics, a unified picture has yet to emerge.…”

Section: Introductionmentioning

confidence: 99%

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

2017

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Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the non-Gaussian fixed points characteristic for Asymptotic Safety the setting exhibits a second family of non-Gaussian fixed points with a positive Newton's constant and real critical exponents. The presence of these new fixed points alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well-defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the -expansion around two dimensions, Monte Carlo simulations based on Lattice Quantum Gravity, and the discretized Wheeler-deWitt equation.

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Euclidian 4d quantum gravity with a non-trivial measure term

Cited by 48 publications

References 55 publications

Lattice quantum gravity and asymptotic safety

Lattice quantum gravity and asymptotic safety

Towards an UV fixed point in CDT gravity

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

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