(geometry Isbell duality algebra)
noncommutative quantum field theory?
It is known since Chu & Ho 1999 (and widely appreciated since Seiberg & Witten 1999) that limits of open string dynamics on D-branes with constant B-field potential effectively yield noncommutative field theories. Specifically, in the default case considered here, of spacelike B-field potential, there exists a clean limit where the string length scale goes to zero, and only point-particle excitations remains.
This is crucially different when the B-field potential has non-vanishing timelike components (corresponding to electric flux density of the Chan-Paton gauge field on the D-brane): In this case (Seiberg, Susskind & Toumbas 2000) there is a limiting critical field value, which keeps the string tension from diverging, while closed string interactions and hence gravity decouples. Therefore at the critical electric field strength one is left (not just with a noncommutative effective field theory but) with a pure open string theory on noncommutative space.
This decoupling limit is hence called noncommutative open string theory, abbreviated NCOS.
At least for open strings on D4-branes, this NCOS has a lift to M-theory (Bergshoeff, Berman, van der Schaar & Sundell 2000), namely to open membranes ending on M5-branes with critical self-dual 3-form flux density.
The corresponding decoupling limit should hence be a noncommutative open membrane theory and as such ought to be abbreviated NCOM but has come to be known just as “OM theory” (GMSS’00, apparently for the sake of the pun).
In this OM theory limit, the angle vanishes between the M5-brane and the open M2-brane that ends on it (Berman & Sundell 2000 §3, Michishita 2000 p 9), making the M2-branes be parallel (lie entirely inside, be dissolved into) the M5 brane (not just their boundary M-strings). Cf. also Hanazawa & Sakaguchi 2018 §4.1.
The original observation of effective noncommutative geometry seen by open strings ending on D-branes with constant B-field gauge potential:
Chong-Sun Chu, Pei-Ming Ho: Noncommutative Open String and D-brane, Nucl. Phys. B 550 (1999) 151-168 [doi:10.1016/S0550-3213(99)00199-6, arXiv:hep-th/9812219]
Volker Schomerus: D-branes and Deformation Quantization, Journal of High Energy Physics 1999 JHEP06 (1999) [doi:10.1088/1126-6708/1999/06/030, arXiv:hep-th/9903205]
Chong-Sun Chu, Pei-Ming Ho: Constrained Quantization of Open String in Background Field and Noncommutative D-brane, Nuclear Physics B 568 1–2 (2000) 447-456 [doi:10.1016/S0550-3213(99)00685-9, arXiv:hep-th/9906192]
Nathan Seiberg, Edward Witten: String Theory and Noncommutative Geometry, Journal of High Energy Physics, 1999 JHEP09 (1999) [doi:10.1088/1126-6708/1999/09/032, arXiv:hep-th/9908142]
The original consideration of electric background flux and its NCOS limit:
Nathan Seiberg, Leonard Susskind, Nicolaos Toumbas: Strings in Background Electric Field, Space/Time Noncommutativity and A New Noncritical String Theory, Journal of High Energy Physics 2000 JHEP06 (2000) [doi:10.1088/1126-6708/2000/06/021, arXiv:hep-th/0005040]
Rajesh Gopakumar, Juan Maldacena, Shiraz Minwalla, Andrew Strominger: S-Duality and Noncommutative Gauge Theory, Journal of High Energy Physics, 2000 JHEP06 (2000) [doi:10.1088/1126-6708/2000/06/036, arXiv:hep-th/0005048]
Review:
Further discussion:
Precursor discussion:
The original discussion of the OM theory lift of NCOS to M-theory:
Eric Bergshoeff, David S. Berman, Jan Pieter van der Schaar, Per Sundell: A Noncommutative M-Theory Five-brane, Nucl. Phys. B 590 (2000) 173-197 [doi:10.1016/S0550-3213(00)00476-4, arXiv:hep-th/0005026]
Rajesh Gopakumar, Shiraz Minwalla, Nathan Seiberg, Andrew Strominger: OM Theory in Diverse Dimensions, Journal of High Energy Physics 2000 JHEP08 (2000) [doi:10.1088/1126-6708/2000/08/008, arXiv:hep-th/0006062]
Eric Bergshoeff, David S. Berman, Jan Pieter van der Schaar, Per Sundell: Critical fields on the M5-brane and noncommutative open strings, Phys. Lett. B 492 (2000) 193-200 [doi:10.1016/S0370-2693(00)01081-9, arXiv:hep-th/0006112]
Further discussion:
J. Antonio Garcia, Alberto Guijosa, J. David Vergara: A Membrane Action for OM Theory, Nuclear Physics B 630 1–2 (2002) 178-202 [doi:10.1016/S0550-3213(02)00175-X, arXiv:hep-th/0201140]
David S. Berman, Per Sundell: Flowing from a noncommmutative (OM) five brane via its supergravity dual, Journal of High Energy Physics 2000 JHEP10 (2000) [doi:10.1088/1126-6708/2000/10/014, arXiv:hep-th/0007052]
Shoichi Kawamoto, Naoki Sasakura: Open membranes in a constant -field background and noncommutative boundary strings, Journal of High Energy Physics 2000 JHEP 07(2000) [doi:10.1088/1126-6708/2000/07/014, arXiv:hep-th/0005123]
Ulf Gran: OM theory, section 8.3 of: The Quest for M-theory, PhD thesis, Göteborg (2001) [pdf, pdf]
Sergei Barakin, Kirill Gubarev, Edvard T. Musaev: Membranes: OM theory, section 3 in: Brane bound states, deformations and OM, Eur. Phys. J. C 86 (2026) 229 [doi:10.1140/epjc/s10052-026-15435-3, arXiv:2511.18899]
Sota Hanazawa, Makoto Sakaguchi: Non-commutative M5-brane, section 4.1 in: Non-commutative M-branes from Open Pure Spinor Supermembrane, Nuclear Physics B 927 (2018) 566-578 [doi:10.1016/j.nuclphysb.2018.01.003, arXiv:1709.03711]
(via pure spinor formalism)
Review:
(focus on the Nambu-Poisson M5-brane model)
The variant of lightlike instead of timelike flux:
and tentatively relating this to engineering of quantum Hall systems:
On the M2/M5-brane interaction angle, generally and in the OM theory limit, where the M2 is parallel to (lies inside, “dissolves” into) the M5
Yoji Michishita; p. 9 of: The M2-brane Soliton on the M5-brane with Constant 3-Form, Journal of High Energy Physics 2000 JHEP09 (2000) [doi:10.1088/1126-6708/2000/09/036, arXiv:hep-th/0008247]
Donam Youm: BPS Solitons in M5-Brane Worldvolume Theory with Constant Three-Form Field, Phys. Rev. D 63 (2001) 045004 [doi:10.1103/PhysRevD.63.045004, arXiv:hep-th/0009082]
Last revised on April 20, 2026 at 20:36:50. See the history of this page for a list of all contributions to it.