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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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