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Noncommutative field theory
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This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level.
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“Other high energy models of spacetime structure, such as non-commutative field theory, do however explicitly contain Lorentz violation [98].”
From Modern Tests of Lorentz Invariance (2005) · cites this paper as [98]
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Noncommutative SO(n) and Sp(n) gauge theories
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Open strings in a B-field background as electric dipoles
Sheikh-Jabbari, M. M. (1999) · Physics Letters B · doi:10.1016/s0370-2693(99)00462-1 · Cited by 109
Noncommutative Geometry Year 2000
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Noncommutative gauge theory for Poisson manifolds
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MORITA EQUIVALENCE OF MULTIDIMENSIONAL NONCOMMUTATIVE TORI
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Hamiltonian formalism for space-time noncommutative theories
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Reduced model for large N continuum field theories
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Exact solution to the Seiberg-Witten equation of noncommutative gauge theory
Okawa, Y., & Ooguri, H. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.64.046009 · Cited by 97
Open string instability in background electric fields
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TRIESTE LECTURES ON SOLITONS IN NONCOMMUTATIVE GAUGE THEORIES
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Noncommutative tachyons and K-theory
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Nielsen-Olesen vortices in noncommutative abelian Higgs model
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The formulation of quantum mechanics in terms of phase space functions
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Open Wilson lines in noncommutative gauge theory and tomography of holographic dual supergravity
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A consistent noncommutative field theory: the Wess–Zumino model
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$D$-brane physics and noncommutative Yang–Mills theory
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Open Wilson Lines in Noncommutative Gauge Theory and Tomography of Holographic Dual SupergravityPreprint
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A Consistent Noncommutative Field Theory: the Wess-Zumino Model
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ON THE ULTRAVIOLET BEHAVIOR OF QUANTUM FIELDS OVER NONCOMMUTATIVE MANIFOLDS
Várilly, J. C., & GRACIA-BONDÍA, J. M. (1999) · International Journal of Modern Physics A · doi:10.1142/s0217751x99000671 · Cited by 77
Poisson sigma models and deformation quantization
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Noncommutative gauge theories in matrix theory
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Critical fields on the M5-brane and noncommutative open strings
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Target space symmetries in topological theories I
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D-Brane Realization of N=2 Super Yang-Mills Theory in Four DimensionsPreprint
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Self-citationEvidence for winding states in noncommutative quantum field theory
Fischler, W., Gorbatov, E., Kashani-Poor, A.-K., Paban, S., Pouliot, P., & Gomis, J. (2000) · Journal of High Energy Physics · doi:10.1088/1126-6708/2000/05/024 · Cited by 69
Integrable systems from gauged matrix models
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Noncommutative geometry and D-branes
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Generalized *-products, Wilson lines and the solution of the Seiberg-Witten equations
Mehen, T., & Wise, M. B. (2000) · Journal of High Energy Physics · doi:10.1088/1126-6708/2000/12/008 · Cited by 69
How noncommutative gauge theories couple to gravity
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Noncommutative geometry on a discrete periodic lattice and gauge theory
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Open branes in space–time non-commutative little string theory
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Noncommutative gauge dynamics from the string worldsheet
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Wilsonian Effective Actions and the IR/UV Mixing in Noncommutative Gauge Theories
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D-branes and Discrete TorsionPreprint
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Self-citationGauge bundles and Born-Infeld on the non-commutative torus
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Non-commutative world-volume interactions on D-brane and Dirac–Born–Infeld action
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A note on consistent anomalies in noncommutative YM theories
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“Topological” Charge of U(1) Instantons on Noncommutative R4
Furuuchi, K. (2001) · Progress of Theoretical Physics Supplement · doi:10.1143/ptps.144.79 · Cited by 56
The Quantum Hall Effect: Novel Excitations and Broken SymmetriesPreprint
Girvin, S. M. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.cond-mat/9907002 · Cited by 56
Wilsonian renormalization group and the non-commutative IR/UV connection
Griguolo, L., & Pietroni, M. (2001) · Journal of High Energy Physics · doi:10.1088/1126-6708/2001/05/032 · Cited by 55
Diagrams of noncommutative Φ3 theory from string theory
Andreev, O., & Dorn, H. (2000) · Nuclear Physics B · doi:10.1016/s0550-3213(00)00326-6 · Cited by 54
Noncommutativity in Space and Primordial Magnetic Field
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Supergravity couplings to Noncommutative Branes, Open Wilson Lines and Generalised Star Products
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Spacetime and fields, a quantum texture
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A note on consistent anomalies in noncommutative YM theories
Bonora, L., Schnabl, M., & Tomasiello, A. (2000) · CERN Document Server (European Organization for Nuclear Research) · Cited by 52
String field theory at large B-field and noncommutative geometry
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Gauge-Invariant Couplings of Noncommutative Branes to Ramond-Ramond BackgroundsPreprint
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String Theory and Noncommutative Field Theories at One Loop
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Noncommutative =1,2 super U(N) Yang–Mills: UV/IR mixing and effective action results at one loop
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Instability of non-commutative SYM theories at finite temperature
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Metadata
- Authors
- Douglas, M., & Nekrasov, N.
- Affiliations
- Rutgers, The State University of New Jersey (US)
- Institute for Theoretical and Experimental Physics (RU)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2001-11
- Volume
- 73
- Issue
- 4
- Pages
- 977-1029
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W1974665356
- Semantic Scholar
- ff829c1cab7a67ce29a3e6216b9b516d6929750f
- Cited by
- 2,096
- References
- 289
- Citations by year
- 2026: 27 · 2025: 46 · 2024: 60 · 2023: 58 · 2022: 49 · 2021: 37 · 2020: 40 · 2019: 66 · 2018: 63 · 2017: 68 · 2016: 84 · 2015: 63 · 2014: 86 · 2013: 85 · 2012: 91
- FWCI
- 89.23
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- noncommutative field theory, noncommutative spacetime, M-theory, string theory, quantum Hall states, noncommutative geometry, classical field theory, quantum field theory
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