3D MANIFOLDS, GRAPH INVARIANTS AND CHERN-SIMONS THEORY
Abstract
We show how the Turaev-Viro invariant, which is closely related to the partition function of three-dimensional gravity, can be understood within the framework of SU(2) Chern-Simons theory. We also show that, for S 3 and RP 3, this invariant is equal to the absolute value square of their respective partition functions in SU(2) Chern-Simons theory and give a method of evaluating the latter in a closed form for a class of 3D manifolds, thus in effect obtaining the partition function of three-dimensional gravity for these manifolds. By interpreting the triangulation of a manifold as a graph consisting of crossings and vertices with three lines we also describe a new invariant for certain class of graphs.
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For a closed three-manifold M, the Turaev-Viro amplitude, interpreted as a partition function, is equal to the absolute square of the partition function of an SU(2) Chern-Simons theory with coupling constant k.
“For a closed three-manifold M, the Turaev-Viro amplitude — now interpreted as a partition function — is equal to the absolute square of the partition function of an SU(2) Chern-Simons theory with coupling constant k [228, 260, 233],”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [228]
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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
- RAMA, S. K., & SEN, S.
- Affiliations
- Tata Institute of Fundamental Research (IN)
- Venue
- Modern Physics Letters A
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1992-07-30
- Volume
- 07
- Issue
- 23
- Pages
- 2065-2076
- ISSN
- 0217-7323 (ISSN-L)
- 1793-6632
- OpenAlex
- W2011372795
- Cited by
- 2
- References
- 0
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Modern Physics Letters A (publishedVersion)
- Topics
- 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
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Keywords
- Turaev-Viro invariants, SU(2) Chern-Simons theory, three-dimensional gravity, partition function, 3-manifolds, S3, RP-3, graph invariants, triangulation, three-manifold invariants
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