2 + 1 dimensional gravity as an exactly soluble system
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Nontrivial spatial or spacetime topologies in 2+1 gravity have moduli that can become dynamical.
“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]
The geometric structure description is closely related to the first-order Chern-Simons formalism, which connects back to the standard metric formalism.
“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]
The first-order action (14) is equivalent to that of a Chern-Simons theory.
“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]
The path integral for the covariant first-order action (14) reduces to a ratio of determinants that has a topological interpretation as the analytic or Ray-Singer torsion.
“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]
This form is unique up to multiplication by a constant factor and defines a dual pairing between so(2,1) and R2+1.
“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]
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 R2+1 and any Levi factor so(2,1) are isotropic.
“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]
Degeneracy is crucial in the canonical partition function calculation of black hole entropy.
“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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Afshar, H. R., Detournay, S., Grumiller, D., Merbis, W., Pérez, A., Tempo, D., & Troncoso, R. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.93.101503 · Cited by 177 · see citing works
Gauge theories and integrable lattice models
Witten, E. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90232-0 · Cited by 177 · see citing works
Self-citationLoop quantum gravity: an outside view
Nicolai, H., Peeters, K., & Zamaklar, M. (2005) · Classical and Quantum Gravity · doi:10.1088/0264-9381/22/19/r01 · Cited by 176 · see citing works
Algebraic structures and differential geometry in two-dimensional string theory
Witten, E., & Barton Zwiebach, C. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90018-7 · Cited by 175 · see citing works
Self-citationTowards integrability for ${\rm Ad}{{{\rm S}}_{{\bf 3}}}/{\rm CF}{{{\rm T}}_{{\bf 2}}}$
Sfondrini, A. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/48/2/023001 · Cited by 173 · see citing works
Quantization of false-vacuum bubbles: A Hamiltonian treatment of gravitational tunneling
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New boundary conditions for AdS3
Compère, G., Song, W., & Strominger, A. (2013) · Journal of High Energy Physics · doi:10.1007/jhep05(2013)152 · Cited by 173 · see citing works
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
What We Don't Know about BTZ Black Hole EntropyPreprint
Carlip, S. J. (1998) · Cited by 172 · see citing works
Relating black holes in two and three dimensions
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- 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 › Statistical and Nonlinear 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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