Exact Three-Dimensional Lattice Gravities
Open accessAbstract
It is shown that the three-dimensional lattice theory defined by Ponzano and Regge is equivalent to the ISO(3) Chern-Simons gauge theory, which is a three-dimensional quantum gravity with Euclidean signature and a zero cosmological constant. And its regularized version defined by Turaev and Viro, which is the q-analogue of the Ponzano-Regge model, is suggested to be equivalent to the SO(4) Chern-Simons gauge theory, which is a three-dimensional quantum gravity with Euclidean signature and a cosmological constant proportional to 1/k2, where q = 2πi/(k+2).
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In the large k limit, the Turaev-Viro Hilbert space is isomorphic to the space of gauge-invariant functions of flat SU(2) connections.
“In the large k limit, the Turaev-Viro Hilbert space is isomorphic to the space of gauge-invariant functions of flat SU(2) connections [219, 220, 242].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [242]
Section 4 identifies the k→∞ Turaev–Viro model with the Ponzano–Regge model and describes the relevant continuum space as gauge-invariant functions of flat SU(2) connections. It concludes that this space is isomorphic to the large-k physical space, but explicitly assumes that the stated Wilson-line-network relations exhaust all linear dependencies. The citing sentence omits that assumption; page numbers were not available in our copy. (LLM, conf=0.84)
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Research works printed but not linked: 23
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Cited by
Sorted by citations
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
- Sasakura, N.
- Affiliations
- Kyoto University (JP)
- Corresponding author
- Sasakura, Naoki
- ORCID
- Sasakura, Naoki
- Venue
- Progress of Theoretical Physics Supplement
- Publisher
- Oxford University Press (OUP)
- Published
- 1992
- Volume
- 110
- Pages
- 191-205
- ISSN
- 0375-9687 (ISSN-L)
- OpenAlex
- W1993961543
- Cited by
- 4
- References
- 0
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Progress of Theoretical Physics Supplement (publishedVersion)
- HighWire Press Open Archive (submittedVersion)
- 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
- Ponzano-Regge model, lattice gravity, three-dimensional quantum gravity, q-deformation, Euclidean signature, cosmological constant, topological field theory, 3-manifold invariants
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