2 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