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Non-commutative solitons and strong-weak duality
High Energy Physics - Theory · Submitted 3 Feb 2005
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The correspondence NCSG$_{1}$ $\leftrightarrow$ NCMT$_{1}$ is promising since it is expected to hold on the quantum level.
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The abstract, sentence by sentence
Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either $U(1){x} U(1)$ or $U(1)_{C}$ corresponding to the Lechtenfeld et al. (NCSG$_{1}$) or Grisaru-Penati (NCSG$_{2}$) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT$_{1, 2}$ models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. The NCATM$_{1,2}$ models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter $\theta$ for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG$_{1}$ $\leftrightarrow$ NCMT$_{1}$ is promising since it is expected to hold on the quantum level.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. | contribution 0.93 | 0.83 | 0.04 | asserted 0.91 |
| s1 | Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. | method 1.00 | 0.51 | 0.03 | asserted 1.00 |
| s2 | The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either $U(1){x} U(1)$ or $U(1)_{C}$ corresponding to the Lechtenfeld et al. (NCSG$_{1}$) or Grisaru-Penati (NCSG$_{2}$) proposals for the NC versions of the sine-Gordon model, respectively. | result 0.48 | 0.73 | 0.10 | asserted 1.00 |
| s3 | Besides, the relevant NCMT$_{1, 2}$ models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. | contribution 0.85 | 0.78 | 0.04 | asserted 1.00 |
| s4 | The NCATM$_{1,2}$ models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter $\theta$ for the corresponding Toda and matter fields describing the strong-weak phases, respectively. | result 1.00 | 0.91 | 0.29 | asserted 1.00 |
| s5 | The correspondence NCSG$_{1}$ $\leftrightarrow$ NCMT$_{1}$ is promising since it is expected to hold on the quantum level. | interpretation 0.95 | 0.18 | 0.42 | hedged possibility 0.92 |
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Original abstract
Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either $U(1){x} U(1)$ or $U(1)_{C}$ corresponding to the Lechtenfeld et al. (NCSG$_{1}$) or Grisaru-Penati (NCSG$_{2}$) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT$_{1, 2}$ models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. The NCATM$_{1,2}$ models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter $\theta$ for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG$_{1}$ $\leftrightarrow$ NCMT$_{1}$ is promising since it is expected to hold on the quantum level.
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How the literature uses it
1 arXiv paper cite this in 6 sentences
Papers citing it · 4 sentences without a confident label
Compares with it 1 paper
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([ref]) then it is reproduced the equation (5.13) of reference [ref] describing the single Thirring field $ψ_3$ provided that the parameters expression $√(δ_3λ_3β_3α_3/16)$ corresponds to the coupling constant $λ/2$ of NCMT model as defined in that reference.
Some comments on the integrability of the noncommutative generalized massive Thirring model · A version of the noncommutative generalized massive Thirring model (NCGMT) · 0.97
Cites it as background 1 paper
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On the other hand, the noncommutative (NC) version of the MT model has been proposed recently [ref] .
Some comments on the integrability of the noncommutative generalized massive Thirring model · Introduction · 0.88
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