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TOPOLOGICAL LATTICE MODELS IN FOUR DIMENSIONS
Open accessAbstract
We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group G. When G= SU (2), the statistical weight is constructed from the 15j-symbol as well as the 6j-symbol for recombination of angular momenta, and the model may be regarded as the four-dimensional version of the Ponzano-Regge model. We show that the partition function of the model is invariant under the Alexander moves of the simplicial complex, thus it depends only on the piecewise linear topology of the manifold. For an orientable manifold, the model is related to the so-called BF model. The q-analog of the model is also constructed, and it is argued that its partition function is invariant under the Alexander moves. It is discussed how to realize the 't Hooft operator in these models associated to a closed surface in four dimensions as well as the Wilson operator associated to a closed loop. Correlation functions of these operators in the q-deformed version of the model would define a new type of invariants of knots and links in four dimensions.
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“More specifically, our expression for the proper time propagator U ( T ) of GR as a sum over worldsheets resembles in many ways the worldsheet sum [8,56] 14 for the projector on physical states, U OCY , of the OCY model.”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [8]
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“BF theory [11] and simplicial GR [8,9] are theories of this kind, and have crossing symmetric vertices.”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [8]
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“There is a natural way of interpreting a branched colored surface σ as a discrete ('quantum') geometry. This geometrical interpretation was proposed in [8] in a slightly different context; it holds in the worldsheet formulation of the simplicial model of GR [9].”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [8]
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Metadata
- Authors
- OOGURI, H.
- Affiliations
- Kyoto University (JP)
- Corresponding author
- OOGURI, HIROSI
- ORCID
- OOGURI, HIROSI
- Venue
- Modern Physics Letters A
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1992-09-28
- Volume
- 07
- Issue
- 30
- Pages
- 2799-2810
- ISSN
- 0217-7323 (ISSN-L)
- 1793-6632
- OpenAlex
- W2171017579
- Cited by
- 379
- References
- 8
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 10 · 2023: 55 · 2022: 5 · 2021: 5 · 2020: 4 · 2019: 9 · 2018: 5 · 2017: 5 · 2016: 29 · 2015: 11 · 2014: 15 · 2013: 24 · 2012: 29
- FWCI
- 9.01
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Modern Physics Letters A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Keywords
- triangulated manifolds, Ponzano-Regge model, 6j symbols, piecewise linear topology, BF model, q-deformation, Wilson loops, SU(2) gauge theory, four-dimensional quantum gravity
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