The DOI matches its Crossref record.
THREE-DIMENSIONAL SIMPLICIAL QUANTUM GRAVITY AND GENERALIZED MATRIX MODELS
Abstract
We consider a discrete model of Euclidean quantum gravity in three dimensions based on a summation over random simplicial manifolds. We derive some elementary properties of the model and discuss possible “matrix” models for 3-D gravity.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Citations
Cites
Still being checked.
Cited by
Sorted by citations
Items 201–300 of 332
A CANONICAL RANK-THREE TENSOR MODEL WITH A SCALING CONSTRAINT
Sasakura, N. (2013) · Institutional Repositories DataBase (IRDB) · Cited by 8
Rivasseau, V. (2013) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/102/61001 · Cited by 9
Correlation functions of $U(N)$-tensor models and their Schwinger–Dyson equations
Pascalie, R., Pérez-Sánchez, C. I., & Wulkenhaar, R. (2021) · Annales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions · doi:10.4171/aihpd/107 · Cited by 8
Emergence of Lie group symmetric classical spacetimes in the canonical tensor model
Kawano, T., & Sasakura, N. (2022) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptac045 · Cited by 8
Renormalization procedure for random tensor networks and the canonical tensor model
Sasakura, N., & Sato, Y. (2015) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptv049 · Cited by 8
Tensorial methods and renormalization
Orsay, L. (2013) · Cited by 7
A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY
Sasakura, N. (2010) · Institutional Repositories DataBase (IRDB) · Cited by 7
Real tensor eigenvalue/vector distributions of the Gaussian tensor model via a four-fermi theory
Sasakura, N. (2022) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptac169 · Cited by 8
Double scaling limit of the prismatic tensor model
Krajewski, T., Müller, T., & Tanasă, A. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/accf4e · Cited by 7
Lattice Quantum Gravity: EDT and CDT
Jan Ambjørn, A. (2023) · Springer eBooks · doi:10.1007/978-981-19-3079-9_84-1 · Cited by 7
A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY
SASAKURA, N. (2010) · International Journal of Modern Physics A · doi:10.1142/s0217751x10050433 · Cited by 7
Quantum field theory on noncommutative spaces
Wulkenhaar, R. (2019) · Springer eBooks · doi:10.1007/978-3-030-29597-4_11 · Cited by 8
Entropy estimates for simplicial quantum gravity
Mauro Carfora, B., & Marzuoli, A. (1995) · Journal of Geometry and Physics · doi:10.1016/0393-0440(94)00022-v · Cited by 7
Recent progress in the theory of random surfaces and simplicial quantum gravity
Jan Ambjørn, A. (1995) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/0920-5632(95)00181-8 · Cited by 8
A two-tensor model with order-three
Kang, B., Wang, L.-Y., Wu, K., & Zhao, W. (2024) · The European Physical Journal C · doi:10.1140/epjc/s10052-024-12568-1 · Cited by 7
Emergent classical geometries on boundaries of randomly connected tensor networks
Chen, H., Sasakura, N., & Sato, Y. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.93.064071 · Cited by 6
Signed distributions of real tensor eigenvectors of Gaussian tensor model via a four-fermi theory
Sasakura, N. (2022) · Physics Letters B · doi:10.1016/j.physletb.2022.137618 · Cited by 7
Sasakura, N. (2023) · Journal of Mathematical Physics · doi:10.1063/5.0133874 · Cited by 7
One-loop beta-functions of quartic enhanced tensor field theories
Geloun, J. B., & Toriumi, R. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/acfdde · Cited by 6
Tensor Models as Theory of Dynamical Fuzzy Spaces and General Relativity
Sasakura, N., & Dobrev, V. K. (2010) · AIP conference proceedings · doi:10.1063/1.3460182 · Cited by 6
Simplical gravity and random surfaces
Jurkiewicz, J. (1993) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/0920-5632(93)90181-5 · Cited by 5
Statistical Hausdorff dimension of labelled trees and quadrangulationsPreprint
Chassaing, P., & Durhuus, B. (2003) · Cited by 6
Self-citationMatter fields in triangle–hinge models
Fukuma, M., Sugishita, S., & Umeda, N. (2016) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptw051 · Cited by 8
Can we make sense out of "Tensor Field Theory"?
Rivasseau, V., & Vignes-Tourneret, F. (2021) · SciPost Physics Core · doi:10.21468/scipostphyscore.4.4.029
Duality of orthogonal and symplectic random tensor models: general invariants
Keppler, H., & Müller, T. (2023) · Letters in Mathematical Physics · doi:10.1007/s11005-023-01706-7 · Cited by 5
Combinatorial Quantum Gravity and Emergent 3D Quantum Behaviour
Trugenberger, C. A. (2023) · Universe · doi:10.3390/universe9120499 · Cited by 5
Trees of Nuclei and Bounds on the Number of Triangulations of the 3-Ball
Collet, P., Eckmann, J., & Younan, M. (2013) · Communications in Mathematical Physics · doi:10.1007/s00220-013-1859-y · Cited by 5
Quantum gravity with linear action and intrinsic rigidity of spacetime
Savvidy, G. K. (1997) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(97)00358-7 · Cited by 5
Sextic tensor model in rank 3 at next-to-leading order
Harribey, S. (2022) · Journal of High Energy Physics · doi:10.1007/jhep10(2022)037 · Cited by 5
Trugenberger, C. A. (2022) · Journal of High Energy Physics · doi:10.1007/jhep04(2022)019 · Cited by 5
The weak-coupling limit of simplicial quantum gravity
Þorleifsson, G., Białas, P., & Petersson, B. (1999) · Nuclear Physics B · doi:10.1016/s0550-3213(99)00140-6 · Cited by 5
Recursive sampling simulations of 3D gravity coupled to scalar fermions
Jan Ambjørn, A., Boulatov, D. V., Kawamoto, N., & Watabiki, Y. (2000) · Physics Letters B · doi:10.1016/s0370-2693(00)00411-1 · Cited by 4
On the Number of Coloured Triangulations of d-Manifolds
Chapuy, G., & Perarnau, G. (2020) · Discrete & Computational Geometry · doi:10.1007/s00454-020-00189-w · Cited by 7
Gibbs, P. (1996) · International Journal of Theoretical Physics · doi:10.1007/bf02302403 · Cited by 5
On the counting tensor model observables as U(N) and O(N) classical invariants
Geloun, J. B. (2020) · Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU) · doi:10.22323/1.376.0175 · Cited by 4
Triangle–hinge models for unoriented membranes
Fukuma, M., Sugishita, S., & Umeda, N. (2016) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptw069 · Cited by 4
Fuzzy spaces from tensor models, cyclicity condition, and n-ary algebras
Sasakura, N. (2012) · doi:10.22323/1.155.0059 · Cited by 4
Real eigenvector distributions of random tensors with backgrounds and random deviations
Sasakura, N. (2023) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptad138 · Cited by 5
Counting $$U(N)^{\otimes r}\otimes O(N)^{\otimes q}$$ invariants and tensor model observables
Avohou, R. C., Geloun, J. B., & Toriumi, R. (2024) · The European Physical Journal C · doi:10.1140/epjc/s10052-024-13091-z · Cited by 4
An OSp extension of the canonical tensor model
Narain, G., & Sasakura, N. (2015) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptv169 · Cited by 4
Signed Eigenvalue/vector Distribution of Complex Order-Three Random Tensor
Sasakura, N. (2024) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptae062 · Cited by 5
Power counting and scaling for tensor models
Krajewski, T., & Toriumi, R. (2016) · doi:10.22323/1.263.0116 · Cited by 4
Blobbed topological recursion for the quartic melonic tensor model
Bonzom, V., & Dartois, S. (2018) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aac8e7 · Cited by 4
A power counting theorem for a $p^{2a}ϕ^4$ tensorial group field theoryPreprint
Geloun, J. B. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1507.00590 · Cited by 7
Noncritical M-theory: Three DimensionsPreprint
McGuigan, M. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0408041 · Cited by 6
Splitting-merging transitions in tensor-vectors systems in exact large- N limits
Sasakura, N. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.126016 · Cited by 3
Asymptotic safety meets tensor field theory: Toward a new class of gravity-matter systems
Eichhorn, A., Gurău, R., & Gyftopoulos, Z. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.085030 · Cited by 5
Usefulness of signed eigenvalue/vector distributions of random tensors
Kloos, M. R., & Sasakura, N. (2024) · Letters in Mathematical Physics · doi:10.1007/s11005-024-01825-9 · Cited by 3
The edge of random tensor eigenvalues with deviation
Delporte, N., & Sasakura, N. (2025) · Journal of High Energy Physics · doi:10.1007/jhep01(2025)071 · Cited by 3
Matrix and tensor witnesses of hidden symmetry algebras
Ramgoolam, S., & Sword, L. (2023) · Journal of High Energy Physics · doi:10.1007/jhep03(2023)056 · Cited by 3
Bounded geometries and topology fluctuations in lattice quantum gravity
Mauro Carfora, B., & Marzuoli, A. (1992) · Classical and Quantum Gravity · doi:10.1088/0264-9381/9/3/005 · Cited by 3
Regularized quantum gravity and string theory
Jan Ambjørn, A. (1992) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(05)80003-9 · Cited by 3
Multimatrix models induced by group extensions
Thomas Filk, A. (1993) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/26/7/020 · Cited by 3
Aspects of quantum gravityPreprint
Pithis, A. G. A. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1903.07735 · Cited by 9
A Givental-like Formula and Bilinear Identities for Tensor ModelsPreprint
Dartois, S. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1409.5621 · Cited by 3
Numerical and analytical studies of a matrix model with non-pairwise contracted indices
Sasakura, N. (2020) · Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU) · doi:10.22323/1.376.0192 · Cited by 2
Jan Ambjørn, A. (1994) · Theoretical and Mathematical Physics · doi:10.1007/bf01102197 · Cited by 2
Narain, G., & Sasakura, N. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa7771 · Cited by 2
Pérez-Sánchez, C. I. (2020) · Mathematical Physics Analysis and Geometry · doi:10.1007/s11040-020-09351-5 · Cited by 3
Review on the operator/Feynman diagram/dessins d’enfants
Itoyama, H., Mironov, A. D., Morozov, A. A., & Yoshioka, R. (2022) · International Journal of Modern Physics A · doi:10.1142/s0217751x21300192 · Cited by 2
Generalized Amit-Roginsky model from perturbations of 3D quantum gravity
Nador, V., Oriti, D., Pang, X., Tanasă, A., & Wang, Y. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.066008 · Cited by 5
Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model
Sasakura, N. (2021) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptab034 · Cited by 2
Backgrounds from tensor models: A proposal
Díaz, P. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.066010 · Cited by 2
Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model
Sasakura, N. (2021) · Institutional Repositories DataBase (IRDB) · Cited by 2
Tensors and Algebras: An Algebraic Spacetime Interpretation for Tensor Models
Obster, D. (2023) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2023.076 · Cited by 2
New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and ApplicationsPreprint
Valette, G. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1911.11574 · Cited by 3
The Tensor Track VII: From Quantum Gravity to Artificial IntelligencePreprint
Ouerfelli, M., Rivasseau, V., & Tamaazousti, M. (2022) · arXiv (Cornell University) · doi:10.48550/arxiv.2205.10326 · Cited by 6
The large N factorization does not hold for arbitrary multi-trace observables in random tensors
Gurău, R., Joos, F., & Benny Sudakov, C. (2025) · Letters in Mathematical Physics · doi:10.1007/s11005-025-01983-4 · Cited by 1
Networks as the fundamental constituents of the Universe
Trugenberger, C. A. (2025) · Journal of Physics Complexity · doi:10.1088/2632-072x/ae29d3 · Cited by 1
Carrozza, S. (2014) · Springer theses · doi:10.1007/978-3-319-05867-2_3 · Cited by 1
Two Paths to Group Field Theories
Carrozza, S. (2014) · Springer theses · doi:10.1007/978-3-319-05867-2_2 · Cited by 1
On-the-fly Optimization of Parallel Computation of Symbolic Symplectic Invariants
Geloun, J. B., Camille Coti, B., & Malony, A. D. (2020) · International Symposium on Parallel and Distributed Computing · doi:10.1109/ispdc51135.2020.00023 · Cited by 1
CANONICAL TENSOR MODEL WITH LOCAL TIME AND ITS UNIQUENESS
Sasakura, N. (2013) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789814518550_0052 · Cited by 1
Goeller, C., Oriti, D., & Schmid, G. (2023) · Annales Henri Poincaré · doi:10.1007/s00023-023-01330-0
Lattice Quantum Gravity: EDT and CDT
Jan Ambjørn, A. (2024) · Springer eBooks · doi:10.1007/978-981-99-7681-2_84 · Cited by 1
Non-perturbative quantum gravity: a conformal perspective
Budd, T. (2012) · Utrecht University Repository (Utrecht University) · Cited by 1
Five Dimensional Dynamical TriangulationsPreprint
George, A. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-lat/9909033 · Cited by 1
Dynamical triangulation with fluctuating topology
de Bakker, B. V. (1995) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/0920-5632(95)00360-l · Cited by 1
Tensor Models: extending the matrix models structures and methodsPreprint
Dartois, S. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1603.02167 · Cited by 1
Quartic Tensor ModelsPreprint
Delepouve, T. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1706.07714 · Cited by 1
The Non-melonic Sector of Tensor Models and GravityPreprint
Díaz, P. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1912.00208 · Cited by 1
Tensor Field Theories: Renormalization and Random GeometryPreprint
Delporte, N. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.07819 · Cited by 1
Neighborly spheres and transversal numbers
Novik, I., & Zheng, H. (2024) · Proceedings of symposia in pure mathematics · doi:10.1090/pspum/110/02015 · Cited by 1
Tensor Models and Group Field Theories: Combinatorics, Large N and Renormalization
Carrozza, S. (2024) · Elsevier eBooks · doi:10.1016/b978-0-323-95703-8.00112-9 · Cited by 12
Combinatorics Of The Hermitian One-Matrix Model
Waters, P. (2015) · UA Campus Repository (The University of Arizona) · Cited by 1
Thomas Filk, A. (1992) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/0920-5632(92)90336-q
A new approach to three-dimensional quantum gravity
Jan Ambjørn, A., & Varsted, S. (1992) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(05)80004-0
Quantization of the canonical tensor model and an exact wave function
Sasakura, N. (2014) · Journal of Physics Conference Series · doi:10.1088/1742-6596/490/1/012014
Renormalizable and asymptotically free tensor field theories
Geloun, J. B. (2016) · MPG.PuRe (Max Planck Society)
Rédacteurs en chef / Chief Editors
Bodineau, T., de Saclay, R., Zambotti, L., de Rédaction, C., Aladi, V. B., Barlow, M. T., Blanchard, G., Collins, B., Corwin, I., Delarue, F., et al. (2014)
Gurău, R. (2016) · doi:10.1093/acprof:oso/9780198787938.003.0010
Gurău, R. (2016) · doi:10.1093/acprof:oso/9780198787938.003.0006
Gurău, R. (2016) · doi:10.1093/acprof:oso/9780198787938.003.0007
Gurău, R. (2016) · doi:10.1093/acprof:oso/9780198787938.003.0009
Embedding Half-Edge Graphs in Punctured SurfacesPreprint
Avohou, R. C., Geloun, J. B., & Hounkonnou, M. N. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1708.08720
The structure of spatial slices of three-dimensional causal triangulationsPreprint
Durhuus, B., & Jónsson, T. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1712.07502
Self-citationThe relation between Geometry and Matter in classical and quantum Gravity and CosmologyPreprint
Regoli, D. (2011) · arXiv (Cornell University) · doi:10.6092/unibo/amsdottorato/3615
Metadata
- Authors
- AMBJØRN, J., DURHUUS, B., & JÓNSSON, T.
- Affiliations
- The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
- University of Copenhagen (DK)
- University of Iceland (IS)
- Venue
- Modern Physics Letters A
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1991-04-20
- Volume
- 06
- Issue
- 12
- Pages
- 1133-1146
- ISSN
- 0217-7323 (ISSN-L)
- 1793-6632
- OpenAlex
- W2139335416
- Cited by
- 341
- References
- 0
- Citations by year
- 2026: 2 · 2025: 8 · 2024: 10 · 2023: 12 · 2022: 13 · 2021: 15 · 2020: 22 · 2019: 18 · 2018: 19 · 2017: 21 · 2016: 37 · 2015: 21 · 2014: 19 · 2013: 25 · 2012: 21
- FWCI
- 6.69
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Modern Physics Letters A (publishedVersion)
- Research at the University of Copenhagen (University of Copenhagen) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- Euclidean quantum gravity, three-dimensional gravity, simplicial manifolds, random simplicial complexes, matrix models, discrete gravity, random geometry
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review