Non-commutative solitons and strong-weak duality

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 $U(1)xU(1)$ 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.

24 pages, 1 fig., LaTex. Typos in star products of eqs. (3.11)-(3.13) and footnote 1 were corrected. Version to appear in JHEP

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• On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• Solitons, kinks and extended hadron model based on the generalized sine-Gordon theory
• Bosonized noncommutative bi-fundamental fermion and S-duality
• Abelian Toda field theories on the noncommutative plane
• About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane
• Some comments on the integrability of the noncommutative generalized massive Thirring model
• Noncommmutative solitons and kinks in the affine Toda model coupled to matter