The DOI matches its Crossref record; 84 of the 84 references it cites were found in a registry or an index.
Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
Open accessAbstract
We study three-dimensional Chern-Simons theory with complex gauge group SL(2,ℂ), which has many interesting connections with three-dimensional quantum gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence of a single knotted Wilson loop in an infinite-dimensional representation of the gauge group, the classical and quantum properties of such theory are described by an algebraic curve called the A-polynomial of a knot. Using this approach, we find some new and rather surprising relations between the A-polynomial, the colored Jones polynomial, and other invariants of hyperbolic 3-manifolds. These relations generalize the volume conjecture and the Melvin-Morton-Rozansky conjecture, and suggest an intriguing connection between the SL(2,ℂ) partition function and the colored Jones polynomial.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Quantum field theory and the Jones polynomial
Witten, E. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01217730 · Cited by 4,758
Black hole in three-dimensional spacetime
Bañados, M., Teitelboim, C., & Zanelli, J. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.1849 · Cited by 3,831
Seiberg, N., & Witten, E. (1994) · Nuclear Physics B · doi:10.1016/0550-3213(94)90124-4 · Cited by 3,729
Quantum Theory of Gravity. I. The Canonical Theory
DeWitt, B. S. (1967) · Physical Review · doi:10.1103/physrev.160.1113 · Cited by 3,385
Hartle, J. B., & Hawking, S. W. (1983) · Physical Review D · doi:10.1103/physrevd.28.2960 · Cited by 3,027
2 + 1 dimensional gravity as an exactly soluble system
Witten, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90143-5 · Cited by 2,562
Geometry of the 2+1 black hole
Bañados, M., Henneaux, M., Teitelboim, C., & Zanelli, J. (1993) · Physical Review D · doi:10.1103/physrevd.48.1506 · Cited by 1,766
A polynomial invariant for knots via von Neumann algebras
Jones, V. F. R. (1985) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-1985-15304-2 · Cited by 1,618
Invariants of 3-manifolds via link polynomials and quantum groups
Reshetikhin, N., & Turaev, V. G. (1991) · Inventiones Mathematicae · doi:10.1007/bf01239527 · Cited by 1,492
Three dimensional manifolds, Kleinian groups and hyperbolic geometry
Thurston, W. P. (1982) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-1982-15003-0 · Cited by 1,350
Cited by
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
Barrett, J. W., & Naish-Guzman, I. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/15/155014 · Cited by 131
Metadata
- Authors
- Gukov, S.
- Venue
- Communications in Mathematical Physics
- Published
- 2005-03-02
- Volume
- 255
- Issue
- 3
- Pages
- 577-627
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W2162715369
- Cited by
- 288
- References
- 84
- FWCI
- 15.80
- Type
- journal article
- Language
- en
- Open access
- green
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 ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial. https://app.cochat.ai/papers/10.1007/s00220-005-1312-y
- The paper
- Gukov, S. (2005). Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial. Communications in Mathematical Physics. https://doi.org/10.1007/s00220-005-1312-y
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
