3D Quantum Gravity and Effective Noncommutative Quantum Field Theory
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We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.
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BF theory with topological defects playing the role of point particles is dual, in a suitable sense, to certain non-commutative field theories in three dimensions.
“These theories have been shown by Freidel and Livine to be dual, in a suitable sense, to certain non-commutative field theories in three dimensions [185, 184].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [184]
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Pachoł, A., & Vitale, P. (2015) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/48/44/445202 · Cited by 25 · see citing works
The area quantum and Snyder space
Romero, J. M., & Zamora, A. (2008) · Physics Letters B · doi:10.1016/j.physletb.2008.02.001 · Cited by 24 · see citing works
κ-Minkowski-deformation of U(1) gauge theory
Kupriyanov, V., Kurkov, M. A., & Vitale, P. (2021) · Journal of High Energy Physics · doi:10.1007/jhep01(2021)102 · Cited by 24 · see citing works
Spinors group field theory and Voros star product: First contact
Dupuis, M., Girelli, F., & Livine, E. R. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.105034 · Cited by 23 · see citing works
Self-citationA 2-categorical state sum model
Baratin, A., & Freidel, L. (2015) · Journal of Mathematical Physics · doi:10.1063/1.4906369 · Cited by 23 · see citing works
Self-citationNote on the geometrical interpretation of quantum groups and noncommutative spaces in gravity
Eugenio Bianchi, A., & Carlo Rovelli, C. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.027502 · Cited by 23 · see citing works
- Authors
- Freidel, L., & Livine, E. R.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-06-07
- Volume
- 96
- Issue
- 22
- Pages
- 221301-221301
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2080465764
- Cited by
- 298
- References
- 13
- Citations by year
- 2026: 4 · 2025: 9 · 2024: 13 · 2023: 13 · 2022: 5 · 2021: 12 · 2020: 6 · 2019: 12 · 2018: 20 · 2017: 21 · 2016: 11 · 2015: 20 · 2014: 18 · 2013: 14 · 2012: 18
- FWCI
- 14.35
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- three-dimensional quantum gravity, noncommutative field theory, κ-deformation, Poincaré group, matter fields, gravitational degrees of freedom, effective field theory
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.
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