A MODEL OF THREE-DIMENSIONAL LATTICE GRAVITY
Open accessAbstract
A model is proposed which generates all oriented 3D simplicial complexes weighted with an invariant associated with a topological lattice gauge theory. When the gauge group is SU q (2), q n =1, it is the Turaev-Viro invariant and the model may be regarded as a nonperturbative definition of 3D simplicial quantum gravity. If one takes a finite Abelian group G, the corresponding invariant gives the rank of the first cohomology group of a complex C:I G (C)=rank(H 1 (C,G)), which means a topological expansion in the Betti number b 1 . In general, it is a theory of the Dijkgraaf-Witten type, i.e., determined completely by the fundamental group of a manifold.
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Freidel and Loupre considered a variant of the Ponzano-Regge model and showed that although the sum over topologies diverges, it is Borel summable.
“Building on work by Boulatov [60], Freidel and Loupre have recently considered a variant of the Ponzano-Regge model, and have shown that although the sum over topologies diverges, it is Borel summable [132].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [60]
From loop quantum gravity and other approaches, the N_i's are naturally related to the area of the faces, and their intertwiner to the volume.
“indeed, we know from loop quantum gravity [3,29] and from other approaches [21], that the N i 's are naturally related to the area of the faces, and their intertwiner to the volume.”
From Barrett–Crane model from a Boulatov–Ooguri field theory over a homogeneous space (2000) · cites this paper as [29]
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- Authors
- BOULATOV, D. V.
- Affiliations
- Commissariat à l'Énergie Atomique et aux Énergies Alternatives (FR)
- Corresponding author
- BOULATOV, D.V.
- Venue
- Modern Physics Letters A
- Publisher
- World Scientific Pub Co Pte Ltd
- Published
- 1992-06-14
- Volume
- 07
- Issue
- 18
- Pages
- 1629-1646
- ISSN
- 0217-7323 (ISSN-L)
- 1793-6632
- OpenAlex
- W2153297565
- Cited by
- 326
- References
- 3
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 10 · 2023: 8 · 2022: 2 · 2021: 34 · 2020: 11 · 2019: 6 · 2018: 6 · 2017: 7 · 2016: 34 · 2015: 15 · 2014: 19 · 2013: 25 · 2012: 26
- FWCI
- 2.81
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Modern Physics Letters A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- simplicial quantum gravity, lattice gauge theory, Turaev-Viro invariants, Dijkgraaf-Witten theory, topological invariants, simplicial complexes, first cohomology group, Betti numbers, non-perturbative quantum gravity, three-dimensional gravity
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