A geometry for multidimensional integrable systems

Strachan, Ian A. B.

doi:10.1016/s0393-0440(96)00019-8

Cited by 51 publications

(68 citation statements)

References 33 publications

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“…where we took into account that both the * and • products collapse into the ordinary product in the classical limit [11]. Provided one appropriately rescales the gauge field, (5) reproduces the Schild action for the relativistic, bosonic string [14,15].…”

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confidence: 99%

Chern–Simons hadronic bag from quenched large-N QCD

2001

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SU(N ) reduced, quenched, gauge theories have been shown to be related to string theories. We extend this result and show how a 4-dimensional, reduced, quenched, Yang-Mills theory, supplemented by the topological term, can be related through the Wigner-Weyl-Moyal correspondence to an open 3-brane model. The boundary of the 3-brane is described by a Chern-Simons 2-brane. We identify the bulk of the 3-brane with the interior of a hadronic bag and the world-volume of the ChernSimons 2-brane with the dynamical boundary of the bag. We estimate the value of the induced bag constant to be a little less than 200 MeV.

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confidence: 99%

Chern–Simons hadronic bag from quenched large-N QCD

2001

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“…where we introduced the •-product which corresponds to the "even" part of the of the * -product [19]. Once each operator is replaced by its own Weyl symbol, the trace operation in Hilbert space turns into an integration over a 2D-dimensional, non-commutative manifold, because of the ubiquitous presence of the * product [20]:…”

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confidence: 99%

p -branes from generalized Yang-Mills theory

Ansoldi

Castro

Spallucci

2001

Class. Quantum Grav.

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Abstract. We consider the reduced, quenched version of a generalized Yang-Mills action in 4k-dimensional spacetime. This is a new kind of matrix theory which is mapped through the Weyl-Wigner-Moyal correspondence into a field theory over a non-commutative phase space. We show that the "classical" limit of this field theory is encoded into the effective action of an open, (4k−1)-dimensional, bulk brane enclosed by a dynamical, Chern-Simons type, (4k − 2)-dimensional, boundary brane. The bulk action is a pure volume term, while the boundary action carries all the dynamical degrees of freedom.

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“…The present discussion reduces to that to NC NLS equation by identifying ∂ w = ∂w. This system is studied in more general framework by Dimakis and Müller-Hoissen and proved to possess infinite conserved quantities [46] in terms of Strachan's product [47].…”

Section: Reduction To Nc Zakharov Systemmentioning

confidence: 99%

Non-commutative Ward's conjecture and integrable systems

Hamanaka

2006

Nuclear Physics B

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Noncommutative Ward's conjecture is a noncommutative version of the original Ward's conjecture which says that almost all integrable equations can be obtained from anti-selfdual Yang-Mills equations by reduction. In this paper, we prove that wide class of noncommutative integrable equations in both (2 + 1)-and (1 + 1)-dimensions are actually reductions of noncommutative anti-self-dual Yang-Mills equations with finite gauge groups, which include noncommutative versions of Calogero-Bogoyavlenskii-Schiff eq., Zakharov system, Ward's chiral and topological chiral models, (modified) Korteweg-de Vries, NonLinear Schrödinger, Boussinesq, N-wave, (affine) Toda, sine-Gordon, Liouville, Tzitzéica, (Ward's) harmonic map eqs., and so on. This would guarantee existence of twistor description of them and the corresponding physical situations in N=2 string theory, and lead to fruitful applications to noncommutative integrable systems and string theories. Some integrable aspects of them are also discussed.

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A geometry for multidimensional integrable systems

Cited by 51 publications

References 33 publications

Chern–Simons hadronic bag from quenched large-N QCD

Chern–Simons hadronic bag from quenched large-N QCD

p -branes from generalized Yang-Mills theory

Non-commutative Ward's conjecture and integrable systems

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