4d Simplicial quantum gravity: matter fields and the corresponding effective action

Bilke, Sven; Burda, Z.; Krzywicki, A.; Petersson, Bengt; J.Tabaczek,; Þorleifsson, Guðmar

doi:10.1016/s0370-2693(98)00675-3

Cited by 40 publications

(74 citation statements)

References 13 publications

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“…The most recent development in this area concerns the addition of non-compact U(1)-gauge fields in the dynamical triangulations approach. The phase structure of these models does indeed appear changed with respect to the pure-gravity models [10], but more recently it has been understood that this is a "spurious" effect, and completely equivalent to a rescaling of the measure by factors of the determinant of the metric [11]. Conflicting numerical results on this issue have been reported at this conference [12], so this may still hold out some hope for more interesting findings in this matter-coupled model.…”

Section: What To Do?mentioning

confidence: 94%

Discrete Lorentzian quantum gravity

Loll¹

2001

Nuclear Physics B - Proceedings Supplements

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Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and that therefore also the lattice theory must be formulated in a background-independent way. After summarizing the status quo of discrete covariant lattice models for four-dimensional quantum gravity, I describe a new class of discrete gravity models whose starting point is a path integral over Lorentzian (rather than Euclidean) space-time geometries. A number of interesting and unexpected results that have been obtained for these dynamically triangulated models in two and three dimensions make discrete Lorentzian gravity a promising candidate for a non-trivial theory of quantum gravity. QUANTUM GRAVITYFor the purposes of this presentation, quantum gravity will be defined as the non-perturbative quantization of the classical theory of general relativity, with and without the inclusion of other matter fields and interactions. Judging from our current knowledge of the fundamental laws of physics, it seems highly likely that at sufficiently large energies also gravitational interactions should be governed by quantum rather than by classical equations of motion. Quantum gravity -whose theoretical formulation is still elusive -should include a consistent description of local quantum phenomena in the presence of strong gravitational fields.It has been known for a long time that perturbative quantum gravity, based on a decompositionof the Lorentzian space-time metric g µν into the flat Minkowski metric η µν and a linear perturbation h µν (representing the degrees of freedom of a massless spin-2 graviton), leads to a nonrenormalizable field theory. Although this does not preclude the use of the perturbation series as an effective description of quantum gravity in the presence of an energy cut-off, it cannot serve as the definition of a fundamental theory. The ensuing need to quantize gravity nonperturbatively is not confined to field theory, but persists in string-theoretic formulations (where it is an unsolved problem as well). Imagine trying to obtain a quantum state representing a 4d Schwarzschild black hole with metricby superposing gravitonic excitations within string theory. However, because of the proportionality G ∼ g 2 str for Newton's constant G [1], this involves arbitrary powers of the string coupling g str , and is therefore an intrinsically nonperturbative construction.1.1. How do we quantize gravity nonperturbatively? The great success of lattice models in describing non-perturbative properties of QCD has for a long time been a motivation for applying discrete methods also in quantum gravity. I will be reporting on the status quo of path-integral ("covariant") lattice models for quantum gravity, and on how to make them more Lorentzian. However, it should be pointed out that there are other ways of tackling the problem, most notably, in a canonical continuum approach based...

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Section: What To Do?mentioning

confidence: 94%

Discrete Lorentzian quantum gravity

Loll¹

2001

Nuclear Physics B - Proceedings Supplements

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“…These results were reproduced by conformal field theory methods (so-called 2D quantum Liouville theory) [7][8][9][10]. For higher dimensional quantum gravity the DT approach has been less successful [11][12][13][14][15][16][17][18][19][20][21]. Firstly, there are only very few analytical results.…”

Section: Introductionmentioning

confidence: 99%

The effective action in 4-dim CDT. The transfer matrix approach

Ambjørn

Gizbert-Studnicki

Görlich

et al. 2014

J. High Energ. Phys.

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Abstract:We measure the effective action in all three phases of 4-dimensional Causal Dynamical Triangulations (CDT) using the transfer matrix method. The transfer matrix is parametrized by the total 3-volume of the CDT universe at a given (discrete) time. We present a simple effective model based on the transfer matrix measured in the de Sitter phase. It allows us to reconstruct the results of full CDT in this phase. We argue that the transfer matrix method is valid not only inside the de Sitter phase ('C') but also in the other two phases. A parametrization of the measured transfer matrix/effective action in the 'A' and 'B' phases is proposed and the relation to phase transitions is explained. We discover a potentially new 'bifurcation' phase separating the de Sitter phase ('C') and the 'collapsed' phase ('B').

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“…It has been shown numerically that simulations using degenerate triangulations lead to a factor of ∼ 10 reduction in finite size effects compared to combinatorial triangulations [15]. We have made various checks of our code against the literature using combinatorial triangulations [16], as well as for degenerate triangulations [11], and good agreement was found.…”

Section: Numerical Implementation and Code Testsmentioning

confidence: 78%

“…We would like to see whether the successes of the CDT formulation can be reproduced using the explicitly covariant EDT formulation. Second, renormalization group studies [9,10] suggest that the ultraviolet critical surface is 3-dimensional, providing the original motivation for revisiting EDT with a third parameter in the bare lattice action [5] [11]. We point out that the CDT action also includes a third parameter, an asymmetry parameter between space and time.…”

Section: Introductionmentioning

confidence: 89%

Exploring the Phase Diagram for Lattice Quantum Gravity

Coumbe

Laiho

2012

Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011)

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We present evidence that a nonperturbative model of quantum gravity defined via Euclidean dynamical triangulations contains a region in parameter space with an extended 4-dimensional geometry when a non-trivial measure term is included in the gravitational path integral. Within our extended region we find a large scale spectral dimension of D s (σ → ∞) = 4.04 ± 0.26 and a Hausdorff dimension that is consistent with D H = 4 from finite size scaling. We find that the short distance spectral dimension is D s (σ → 0) ≈ 3/2, which may resolve the tension between asymptotic safety and holographic entropy scaling.

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4d Simplicial quantum gravity: matter fields and the corresponding effective action

Cited by 40 publications

References 13 publications

Discrete Lorentzian quantum gravity

Discrete Lorentzian quantum gravity

The effective action in 4-dim CDT. The transfer matrix approach

Exploring the Phase Diagram for Lattice Quantum Gravity

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