Bosonized noncommutative bi-fundamental fermion and S-duality

We perform the path-integral bosonization of the recently proposed noncommutative massive Thirring model (NCMT$_{1}$) [JHEP0503(2005)037]. This model presents two types of current-current interaction terms related to the bi-fundamental representation of the group U(1). Firstly, we address the bosonization of a bi-fundamental free Dirac fermion defined on a noncommutative (NC) Euclidean plane \IR_{\theta}^{2}. In this case we show that the fermion system is dual to two copies of the NC Wess-Zumino-Novikov-Witten model. Next, we apply the bosonization prescription to the NCMT$_{1}$ model living on \IR_{\theta}^{2} and show that this model is equivalent to two-copies of the WZNW model and a two-field potential defined for scalar fields corresponding to the global $U(1)\times U(1)$ symmetry plus additional bosonized terms for the four fermion interactions. The bosonic sector resembles to the one proposed by Lechtenfeld et al. [Nucl. Phys. B705(2005)477] as the noncommutative sine-Gordon for a {\sl pair} of scalar fields. The bosonic and fermionic couplings are related by a strong-weak duality. We show that the couplings of the both sectors for some representations satisfy similar relationships up to relevant re-scalings, thus the NC bi-fundamental couplings are two times the corresponding ones of the NC fundamental (anti-fundamental) and eight times the couplings of the ordinary massive Thirring and sine-Gordon models.Comment: 18 pages, LaTex. References added. A general product $f(x-vt) \star g(x-vt)$ has been considered in the conclusion section . Version to appear in JHE

Bosonization and generalized Mandelstam soliton operators

The generalized massive Thirring model (GMT) with three fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized sine-Gordon model (GSG) with three interacting soliton species. The generalized Mandelstam soliton operators are constructed and the fermion-boson mapping is established through a set of generalized bosonization rules in a quotient positive definite Hilbert space of states. Each fermion species is mapped to its corresponding soliton in the spirit of particle/soliton duality of Abelian bosonization. In the semi-classical limit one recovers the so-called SU(3) affine Toda model coupled to matter fields (ATM) from which the classical GSG and GMT models were recently derived in the literature. The intermediate ATM like effective action possesses some spinors resembling the higher grading fields of the ATM theory which have non-zero chirality. These fields are shown to disappear from the physical spectrum, thus providing a bag model like confinement mechanism and leading to the appearance of the massive fermions (solitons). The ordinary MT/SG duality turns out to be related to each SU(2) sub-group. The higher rank Lie algebra extension is also discussed.Comment: 22 pages, LaTex. Some misprints were corrected. Published in Eur.Phys J.

Non-commutative solitons and strong-weak duality

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

Generalized sine-Gordon/massive Thirring models and soliton/particle correspondences

We consider a real Lagrangian off-critical submodel describing the soliton sector of the so-called conformal affine $sl(3)^{(1)}$ Toda model coupled to matter fields (CATM). The theory is treated as a constrained system in the context of Faddeev-Jackiw and the symplectic schemes. We exhibit the parent Lagrangian nature of the model from which generalizations of the sine-Gordon (GSG) or the massive Thirring (GMT) models are derivable. The dual description of the model is further emphasized by providing the relationships between bilinears of GMT spinors and relevant expressions of the GSG fields. In this way we exhibit the strong/weak coupling phases and the (generalized) soliton/particle correspondences of the model. The $sl(n)^{(1)}$ case is also outlined.Comment: 22 pages, LaTex, some comments and references added, conclusions unchanged, to appear in J. Math. Phy