The DOI matches its Crossref record; 27 of the 28 references it cites were found in a registry or an index.
2 + 1 dimensional gravity as an exactly soluble system
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In the citing paper
“One can consider nontrivial spatial or spacetime topologies [277, 279]. Such “cosmological” solutions have moduli — a finite number of parameters that distinguish among geometrically inequivalent constant curvature manifolds — and these can become dynamical.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [277]
In the citing paper
“Fortunately, the description is closely related to the more familiar first-order Chern-Simons formalism [108, 277, 279, 2], which, in turn, can connect us back to the standard metric formalism.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [277]
In the citing paper
“As first noted by Achúcarro and Townsend [2] and further developed by Witten [277, 279], the first-order action (14) is equivalent to that of a Chern-Simons theory.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [277]
In the citing paper
“The path integral for this action was first fully analyzed in two seminal papers by Witten [277, 279], who showed that it reduced to a ratio of determinants that has an elegant topological interpretation as the analytic or Ray-Singer torsion [230].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [277]
In the citing paper
“this form is unique up to multiplication by a constant factor and defines a dual pairing between so (2 , 1) and R 2+1 .”
From Lorentz spacetimes of constant curvature (2007) · cites this paper as [2]
In the citing paper
“Witten's paper [2] contains the result that the Einstein equation R ij = 0 can be regarded as the Euler-Lagrange equations for the Chern-Simons form 〈 A,dA + 2 3 [ A,A ] 〉 where A is an ISO (2 , 1) connection and 〈 , 〉 is the invariant bilinear form on the Lie algebra iso (2 , 1) for which both the radical R 2+1 and any Levi factor so (2 , 1) are isotropic”
From Lorentz spacetimes of constant curvature (2007) · cites this paper as [2]
In the citing paper
“The degeneracy plays a crucial role in the calculation [27,28] of black hole entropy using a canonical partition function approach.”
From Symmetry reduction for quantized diffeomorphism-invariant theories of connections (2000) · cites this paper as [28]
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Metadata
- Authors
- Witten, E.
- Affiliations
- Princeton University (US)
- Corresponding author
- Witten, Edward
- ORCID
- Witten, Edward
- Venue
- Nuclear Physics B
- Publisher
- Elsevier BV
- Published
- 1988-12
- Volume
- 311
- Issue
- 1
- Pages
- 46-78
- ISSN
- 0550-3213 (ISSN-L)
- OpenAlex
- W2025148421
- Cited by
- 2,562
- References
- 28
- Citations by year
- 2026: 45 · 2025: 91 · 2024: 82 · 2023: 135 · 2022: 94 · 2021: 68 · 2020: 111 · 2019: 89 · 2018: 90 · 2017: 79 · 2016: 97 · 2015: 87 · 2014: 98 · 2013: 96 · 2012: 80
- FWCI
- 40.01
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Nuclear Physics B (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- three-dimensional gravity, Chern-Simons gravity, Yang-Mills theory, beta function, classical singularities, solid geometry, cosmological constant
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