3-Dimensional Gravity and the Turaev-Viro Invariant
Abstract
We derived an asymptotic formula for q -6 j symbol. This is a generalization of the former work by Ponzano and Regge. Studying the q -deformed su (2) spin network as a 3-dimensional quantum gravity model, we show that the Turaev-Viro invariant defines naturally regularized path-integral à la Ponzano-Regge in the semi-classical continuum limit. We find a term which should be related to the cosmological constant term in 3-dimensional gravity. The contribution from the cosmological term is effectively included in the path-integral from the invariant, and the cosmological constant is found to be 4π2/ k 2+O( k −4), where q 2 k = 1. We point out also that the duality matrices of the su (2) WZW model may be identified as the Turaev-Viro invariant evaluated on a certain 3-manifold.
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For large but finite k, the Turaev-Viro quantum group regularization introduces a cosmological constant to the Regge action, Λ(4π/k)^2.
“For large but finite k, the Turaev-Viro quantum group regularization introduces a cosmological constant to the Regge action [204, 203],”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [203]
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Quantum 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
- Mizoguchi, S., & Tada, T.
- Affiliations
- Kyoto University (JP)
- Venue
- Progress of Theoretical Physics Supplement
- Publisher
- Oxford University Press (OUP)
- Published
- 1992
- Volume
- 110
- Pages
- 207-227
- ISSN
- 0375-9687 (ISSN-L)
- OpenAlex
- W2962963800
- Cited by
- 11
- References
- 0
- Citations by year
- 2018: 1 · 2015: 2
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Progress of Theoretical Physics Supplement (publishedVersion)
- HighWire Press Open Archive (submittedVersion)
- Funders
- Japan Society for the Promotion of Science
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- Turaev-Viro invariants, Ponzano-Regge model, spin networks, cosmological constant, Wess-Zumino-Witten model, 3-manifolds
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