Three-dimensional gravity from the Turaev-Viro invariant
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We study the q-deformed su(2) spin network as a three-dimensional quantum gravity model. We show that in the semiclassical continuum limit the Turaev-Viro invariant obtained recently defines a naturally regularized path integral a` la Ponzano and Regge, in which a contribution from the cosmological term is effectively included. The regularization-dependent cosmological constant is found to be 4${\mathrm{\ensuremath{\pi}}}^{2}$/${\mathit{k}}^{2}$+O(${\mathit{k}}^{\mathrm{\ensuremath{-}}4}$), where ${\mathit{q}}^{2\mathit{k}}$=1. We also discuss the relation to the Euclidean Chern-Simons-Witten gravity in three dimensions.
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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 [204]
The abstract says the Turaev–Viro path integral effectively includes a cosmological term, and the discussion following Eq. (35) describes it as a regularization counterterm in the large-k approximation. But the abstract gives the cosmological constant as 4π²/k² + O(k⁻⁴), not (4π/k)²; Eq. (35) is consistent with the abstract’s value. (LLM, conf=0.90)
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2 + 1 dimensional gravity as an exactly soluble system
Witten, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90143-5 · Cited by 2,562 · see citing works
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Research works printed but not linked: 2
- [5][5] V. G. Turaev and O. Y. Viro, LOMI preprint.
- [6][6] A. N. Kirillov and N. Yu. Reshetikhin, in Adv. Ser. in Math. Phys, ed. G. Kac, vol. 7 (1988).
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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
Diffeomorphisms and spin foam models
Freidel, L., & Louapre, D. (2003) · Nuclear Physics B · doi:10.1016/s0550-3213(03)00306-7 · Cited by 155 · see citing works
- Authors
- Mizoguchi, S., & Tada, T.
- Affiliations
- Kyoto University (JP)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1992-03-23
- Volume
- 68
- Issue
- 12
- Pages
- 1795-1798
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2050785146
- Cited by
- 83
- References
- 1
- Citations by year
- 2025: 1 · 2024: 1 · 2022: 1 · 2021: 2 · 2020: 3 · 2019: 2 · 2018: 4 · 2017: 5 · 2016: 3 · 2015: 6 · 2014: 8 · 2013: 3 · 2012: 3
- FWCI
- 3.74
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- 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 › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- Turaev-Viro invariants, three-dimensional quantum gravity, spin networks, Ponzano-Regge model, cosmological constant, quantum groups
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