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Non-perturbative 3d Lorentzian Quantum Gravity
High Energy Physics - Theory · Submitted 29 Nov 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim These findings provide further evidence that discrete {\it Lorentzian} gravity is a promising candidate for a non-trivial theory of quantum gravity.
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The abstract, sentence by sentence
We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized non-perturbative state sum over simplicial Lorentzian space-times, each possessing a unique Wick rotation to Euclidean signature. We investigate here the phase structure of the Wick-rotated path integral in three dimensions with the aid of computer simulations. After fine-tuning the cosmological constant to its critical value, we find a whole range of the gravitational coupling constant $k_0$ for which the functional integral is dominated by non-degenerate three-dimensional space-times. We therefore have a situation in which a well-defined ground state of extended geometry is generated dynamically from a non-perturbative state sum of fluctuating geometries. Remarkably, its macroscopic scaling properties resemble those of a semi-classical spherical universe. Measurements so far indicate that $k_0$ defines an overall scale in this extended phase, without affecting the physics of the continuum limit. These findings provide further evidence that discrete {\it Lorentzian} gravity is a promising candidate for a non-trivial theory of quantum gravity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized non-perturbative state sum over simplicial Lorentzian space-times, each possessing a unique Wick rotation to Euclidean signature. | background 0.55 | 0.77 | 0.05 | asserted 1.00 |
| s1 | We investigate here the phase structure of the Wick-rotated path integral in three dimensions with the aid of computer simulations. | contribution 0.58 | 0.90 | 0.02 | asserted 0.86 |
| s2 | After fine-tuning the cosmological constant to its critical value, we find a whole range of the gravitational coupling constant $k_0$ for which the functional integral is dominated by non-degenerate three-dimensional space-times. | result 1.00 | 0.97 | 0.19 | asserted 1.00 |
| s3 | We therefore have a situation in which a well-defined ground state of extended geometry is generated dynamically from a non-perturbative state sum of fluctuating geometries. | interpretation 0.94 | 0.88 | 0.45 | asserted 1.00 |
| s4 | Remarkably, its macroscopic scaling properties resemble those of a semi-classical spherical universe. | result 0.86 | 0.88 | 0.11 | asserted 0.93 |
| s5 | Measurements so far indicate that $k_0$ defines an overall scale in this extended phase, without affecting the physics of the continuum limit. | result 0.92 | 0.90 | 0.09 | hedged possibility 0.90 |
| s6 | These findings provide further evidence that discrete {\it Lorentzian} gravity is a promising candidate for a non-trivial theory of quantum gravity. | interpretation 1.00 | 0.60 | 0.72 | hedged possibility 0.86 |
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The paper
Original abstract
We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized non-perturbative state sum over simplicial Lorentzian space-times, each possessing a unique Wick rotation to Euclidean signature. We investigate here the phase structure of the Wick-rotated path integral in three dimensions with the aid of computer simulations. After fine-tuning the cosmological constant to its critical value, we find a whole range of the gravitational coupling constant $k_0$ for which the functional integral is dominated by non-degenerate three-dimensional space-times. We therefore have a situation in which a well-defined ground state of extended geometry is generated dynamically from a non-perturbative state sum of fluctuating geometries. Remarkably, its macroscopic scaling properties resemble those of a semi-classical spherical universe. Measurements so far indicate that $k_0$ defines an overall scale in this extended phase, without affecting the physics of the continuum limit. These findings provide further evidence that discrete {\it Lorentzian} gravity is a promising candidate for a non-trivial theory of quantum gravity.
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References
How the literature uses it
15 arXiv papers cite this in 46 sentences
Papers citing it · 28 sentences without a confident label
Uses its method or tool 4 papers
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Some previously existing code for the Monte Carlo simulations (used in [ref] ) was adapted for this purpose.
Spectral geometry as a probe of quantum spacetime · Application of spectral geometry to CDTs · 1.00
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The basic set of moves we used is shown in Fig. [ref], see also [ref] .
Zooming in on the Universe: In Search of Quantum Spacetime · Implementation · 0.94
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An adaptation of some previously existing code for the Monte Carlo simulations (used in [ref] ) was used for this purpose.
Landau Theory of Causal Dynamical Triangulations · Spatial volume dynamics in three-dimensional CDT · 1.00
Compares with it 2 papers
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It should be mentioned that to the best of our knowledge, this is the largest system size ever reported for (2+1)-dimensional CDT ( [ref] reached 64k at most, and [ref] reached 102k), and so we hope that we shall be forgiven for not pushing the simulations even further.
Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model · Comparison between the HL-minisuperspace model and CDT · 0.80
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Just like standard CDT in three dimensions [ref] , the system exhibits a phase transition as a function of $k$, with a physical, “de Sitter-like" phase at low vertex density $N_0/N_3$ for $k < k^crit≈ 0.25$, and one at high vertex density above.
Quantum Gravity from Causal Dynamical Triangulations: A Review · Causal structure, Wick rotation, time and all that · 0.95
Cites it as background 7 papers
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Simulations of 3D CDT have demonstrated the existence of two distinct geometric phases [ref] .
The phase structure and effective action of 3D CDT at higher spatial genus · Phase structure · 0.87
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introduced in: [ref] coupling to matter: [ref] [ref] [ref] recently [ref] Benedetti:2006rv relation to Euclidean theory [ref] [ref] [ref] summary: [ref] generalizations [ref] [ref] higher dimensional formalism: [ref] [ref] three d computer simulations: [ref] [ref] three d analytical [ref] [ref] [ref] recently [ref] CDT solves conformal factor problem and continuum interpretation of Wick rotation, [ref] [ref] [ref] lecture notes: [ref] four d results computer sims: [ref] [ref] [ref] [ref] [ref] [ref]
Topology Change and the Emergence of Geometry in Two Dimensional Causal Quantum Gravity · Causal dynamical triangulations · 0.98
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CDT in 2+1 dimensions is so far not solvable, and its properties have also been studied mostly by numerical simulations [ref] , but one can in principle reach larger volumes than in higher dimensions, and furthermore some analytical tools are available [ref] (and others might be developed more likely than in higher dimensions).
Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model · Introduction · 0.91
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