Nonperturbative 3D Lorentzian quantum gravity
Open accessAbstract
We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized nonperturbative state sum over simplicial Lorentzian space-times, each possessing a unique Wick rotation to the 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 nondegenerate three-dimensional space-times. We therefore have a situation in which a well-defined ground state of extended geometry is generated dynamically from a nonperturbative state sum of fluctuating geometries. Remarkably, its macroscopic scaling properties resemble those of a semiclassical 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 Lorentzian gravity is a promising candidate for a nontrivial theory of quantum gravity.
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At strong coupling, the Lorentzian dynamical triangulation system splits into uncorrelated two-dimensional spaces, each well-described by two-dimensional gravity.
“At strong coupling, the system splits into uncorrelated two-dimensional spaces, each well-described by two-dimensional gravity.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [12]
Section 4.1 (pp. 15, 18) describes uncorrelated two-dimensional spatial geometries for k₀ above its critical value and suggests they behave as uncoupled 2D gravity models. But the Introduction (p. 5) defines k₀ as proportional to the inverse gravitational coupling, so this is the weak-gravitational-coupling regime, not the strong-coupling regime claimed. (LLM, conf=0.86)
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Experimental — accuracy not yet measuredIn (2+1)-dimensional Lorentzian dynamical triangulation models, the wrong-sign contributions are unimportant because they are overwhelmed by the larger number of well-behaved geometries.
“In the (2 + 1)-dimensional Lorentzian dynamical triangulation models of Section 3.7, however, it is known that these wrong sign contributions are unimportant[12]; they are overwhelmed by the much larger number of well-behaved geometries in the path integral.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [12]
In §5 (p. 26), the paper reports an extended phase with a well-defined ground state and says entropy contributions apparently outbalance potential conformal divergences from the Wick-rotated action. This supports the proposed mechanism, but the citing sentence presents it as an established result for the models generally, whereas the paper qualifies it as an inference about a particular phase. (LLM, conf=0.84)
Experimental — accuracy not yet measuredIn the Lorentzian dynamical triangulation model, expectation value of spatial area at fixed time and correlation of successive areas match classical de Sitter behavior for a spacetime R×S2 quite well.
“In particular, one may evaluate the expectation value 〈A(t)〉 of the spatial area at fixed time and the correlation 〈A(t)A(t + 1)〉 of successive areas; the results match the classical de Sitter behavior for a spacetime ℝ × S2 quite well.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [12]
The Numerical Results section (p. 13) says the model measures spatial slice-volumes and correlations between them. In the extended phase (pp. 20–21), the measured correlator fits a classical Euclidean three-sphere modified with a thin stalk rather well. The paper does not report a match to Lorentzian de Sitter behavior on ℝ × S², nor establish the claimed match for both the fixed-time expectation value and successive-area correlation. (LLM, conf=0.86)
Experimental — accuracy not yet measuredAt weak coupling, a semiclassical regime appears that resembles the picture obtained from other approaches to (2+1)-dimensional gravity.
“At weak coupling, however, a “semiclassical” regime appears that resembles the picture obtained from other approaches to (2 + 1)-dimensional gravity.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [12]
Section 4.2 (pp. 19–21) reports semiclassical macroscopic behavior, but places it in the phase of intermediate gravitational coupling, not the weak-coupling phase. Section 4.1 (p. 18) says the weak-coupling phase consists of uncorrelated two-dimensional geometries rather than a three-dimensional gravity theory. The discussion of canonical approaches in Section 5 (p. 27) says the authors lack observables for a comparison with their spherical-slice model, so resemblance to a picture from other approaches is not established. (LLM, conf=0.86)
Experimental — accuracy not yet measuredIn the Lorentzian dynamical triangulation model, the path integral can be evaluated numerically using Monte Carlo methods and moves that systematically change an initial triangulation; one finds two phases.
“The path integral for such a system can be evaluated numerically, using Monte Carlo methods and a set of “moves” that systematically change an initial triangulation [12, 10]. One finds two phases.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [12]
The alternative Lorentzian model introduced by Ambjørn and Loll has much nicer properties, including a continuum limit that appears numerically to match a finite-sized, spherical semiclassical configuration.
“An alternative “Lorentzian” model, introduced by Ambjørn and Loll [16, 9, 12, 10, 180, 13], however, has much nicer properties, including a continuum limit that appears numerically to match a finite-sized, spherical “semiclassical” configuration.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [12]
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Cites
Four-dimensional simplicial quantum gravity
Ambjørn, J., & Jurkiewicz, J. (1992) · Physics Letters B · doi:10.1016/0370-2693(92)90709-d · Cited by 205 · see citing works
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Research works printed but not linked: 23
- [1][1] J. Ambjørn: Quantization of geometry, in: Fluctuating geometries in statistical mechanics and field theory (Les Houches Summer School, Session LXII, 1994) , eds. F. David, P. Ginsparg and J. Zinn-Justin, (Elsevier, Amsterdam, 1996) 77-193 [hep-th/9411179]. - · arXiv
- [3][3] R. Loll: Discrete approaches to quantum gravity in four dimensions, Living Rev. Rel. 1 (1998) 13, http://www.livingreviews.org/Articles/Volume1/199813loll [gr-qc/9805049]. - · arXiv
- [4][4] J. Ambjørn and R. Loll: Non-perturbative Lorentzian quantum gravity, causality and topology change, Nucl. Phys. B 536 (1998) 407-434 [hep-th/9805108]. - · arXiv
- [5][5] J. Ambjørn, J. Jurkiewicz and R. Loll: A nonperturbative Lorentzian path integral for gravity, Phys. Rev. Lett. 85 (2000) 924-927 [hep-th/0002050]. - · arXiv
- [6][6] J. Ambjørn, J. Jurkiewicz and R. Loll: Dynamically triangulating Lorentzian quantum gravity, preprint Golm AEI-2001-049. -
- [7][7] J. Ambjørn, R. Loll, J.L. Nielsen and J. Rolf: Euclidean and Lorentzian quantum gravity - lessons from two dimensions, J. Chaos Solitons Fractals 10 (1999) 177-195 [hep-th/9806241]. - · arXiv
- [9][9] J. Ambjørn, K.N. Anagnostopoulos and R. Loll: Crossing the c=1 barrier in 2d Lorentzian quantum gravity, Phys. Rev. D 61 (2000) 044010 [hep-lat/9909129]. - · arXiv
- [10][10] J. Ambjørn, J. Jurkiewicz and R. Loll: Computer simulations of 3d Lorentzian quantum gravity, Nucl. Phys. B (Proc. Suppl.) 94 (2001) 689-692 [heplat/0011055]. -
- [11][11] R. Loll: Discrete Lorentzian quantum gravity, Nucl. Phys. B (Proc. Suppl.) 94 (2001) 96-107 [hep-th/0011194]. - · arXiv
- [12][12] R. Loll: Quantum aspects of 2+1 gravity, J. Math. Phys. 36 (1995) 6494-6509 [gr-qc/9503051]. - · arXiv
- [13][13] S. Carlip, Quantum Gravity in 2+1 Dimensions (Cambridge University Press, Cambridge, 1998). -
- [15][15] F. David: Simplicial quantum gravity and random lattices, in: Gravitation and quantizations (Les Houches Summer School, Session LVII, 1992) , eds. J. ZinnJustin and B. Julia (Elsevier, Amsterdam, 1995) 679-750 [hep-th/9303127]. - · arXiv
- [17][17] J. Ambjørn, J. Jurkiewicz and R. Loll: Lorentzian and Euclidean quantum gravity - analytical and numerical results, in: M-Theory and Quantum Geometry , eds. L. Thorlacius and T. Jonsson, NATO Science Series (Kluwer Academic Publishers, 2000) 382-449 [hep-th/0001124]. - · arXiv
- [20][20] H. Kawai, Y. Kitazawa and M. Ninomiya: Ultraviolet stable fixed point and scaling relations in (2+epsilon)-dimensional quantum gravity, Nucl. Phys. B 404 (1993) 684-714 [hep-th/9303123]. - · arXiv
- [21][21] H. Kawai, Y. Kitazawa and M. Ninomiya: Renormalizability of quantum gravity near two-dimensions, Nucl. Phys. B 467 (1996) 313-331 [hep-th/9511217]. - · arXiv
- [22][22] J. Ambjørn, J. Jurkiewicz, R. Loll and G. Vernizzi: Lorentzian 3d gravity with wormholes via matrix models, preprint AEI Golm, to appear. -
- [23][23] A. Dasgupta and R. Loll: A proper-time cure for the conformal sickness in quantum gravity, Nucl. Phys. B , to appear [hep-th/0103186]. - · arXiv
- [24][24] H. Kawai, N. Kawamoto, T. Mogami and Y. Watabiki: Transfer matrix formalism for two-dimensional quantum gravity and fractal structures of space-time, Phys. Lett. B 306 (1993) 19-26 [hep-th/9302133]. - · arXiv
- [25][25] J. Ambjørn and Y. Watabiki: Scaling in quantum gravity, Nucl. Phys. B 445 (1995) 129-144 [hep-th/9501049]. - · arXiv
- [26][26] J. Ambjørn and J. Jurkiewicz: Scaling in four dimensional quantum gravity, Nucl. Phys. B 451 (1995) 643-676 [hep-th/9503006]; J. Ambjørn, J. Jurkiewicz and Y. Watabiki: On the fractal structure of two-dimensional quantum gravity, Nucl. Phys. B 454 (1995) 313-342 [hep-lat/9507014]. - · arXiv
- [27][27] S. Catterall, G. Thorleifsson, M. Bowick and V. John: Scaling and the fractal geometry of two-dimensional quantum gravity, Phys. Lett. B 354 (1995) 58-68 [hep-lat/9504009]. - · arXiv
- [30][30] R. Nakayama: 2-d quantum gravity in the proper time gauge, Phys. Lett. B 325 (1994) 347-353 [hep-th/9312158]. - · arXiv
- [31][31] J. Ambjørn, J. Correia, C. Kristjansen and R. Loll: The relation between Euclidean and Lorentzian 2D quantum gravity, Phys. Lett. B 475 (2000) 24-32 [hep-th/9912267]. · arXiv
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Quantum gravity from causal dynamical triangulations: a review
Loll, R. (2020) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab57c7 · Cited by 359 · see citing works
Self-citationQuantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
- Authors
- Ambjørn, J., Jurkiewicz, J., & Loll, R.
- Affiliations
- University of Copenhagen (DK)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2001-07-24
- Volume
- 64
- Issue
- 4
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2038018081
- Cited by
- 116
- References
- 1
- Citations by year
- 2025: 3 · 2024: 5 · 2023: 2 · 2022: 3 · 2021: 2 · 2020: 2 · 2019: 3 · 2018: 1 · 2017: 4 · 2016: 4 · 2015: 5 · 2014: 6 · 2013: 5 · 2012: 8
- FWCI
- 5.89
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
- Max Planck Institute for Plasma Physics (submittedVersion)
- Max Planck Digital Library (submittedVersion, other-oa)
- Research at the University of Copenhagen (University of Copenhagen) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- European Social Fund
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- Lorentzian quantum gravity, discrete gravity, simplicial geometry, state sum models, Wick rotation, phase structure, cosmological constant, gravitational coupling constant, ground state, three-dimensional gravity
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