1,569 research outputs found
Bosonized noncommutative bi-fundamental fermion and S-duality
We perform the path-integral bosonization of the recently proposed
noncommutative massive Thirring model (NCMT) [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 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 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 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 or corresponding
to the Lechtenfeld et al. (NCSG) or Grisaru-Penati (NCSG) proposals
for the NC versions of the sine-Gordon model, respectively. Besides, the
relevant NCMT 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 models share the same
one-soliton (real Toda field sector of model 2) exact solutions, which are
found without expansion in the NC parameter for the corresponding Toda
and matter fields describing the strong-weak phases, respectively. The
correspondence NCSG NCMT 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 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 case is also
outlined.Comment: 22 pages, LaTex, some comments and references added, conclusions
unchanged, to appear in J. Math. Phy
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