Bosonized noncommutative bi-fundamental fermion and S-duality

Abstract

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 $\IR_θ^{2}$. 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 $\IR_θ^{2}$ 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.

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 JHEP

References in corpus (39)

• String Theory and Noncommutative Geometry
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• D-branes and the Noncommutative Torus
• Space-Time Noncommutative Field Theories And Unitarity
• Space/Time Non-Commutativity and Causality
• S-Duality and Noncommutative Gauge Theory
• Chiral Gauge Anomalies on Noncommutative R^4
• Bosonization as Duality
• A Note on Superfields and Noncommutative Geometry
• Anti-self-dual Yang-Mills equations on noncommutative spacetime
• Duality and Non-Commutative Gauge Theory
• Axial Anomaly in Noncommutative QED on R^4
• NCOS and D-branes in Time-dependent Backgrounds
• Affine Toda Systems Coupled to Matter Fields
• Noncommutative and Ordinary Super Yang-Mills on (D$(p-2)$, D$p$) Bound States
• Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories
• Integrable Noncommutative Sine-Gordon Model
• Noncommutative Integrable Field Theories in 2d
• Nonabelian Bosonization as Duality
• Open N=2 strings in a B-field background and noncommutative self-dual Yang-Mills
• Wess-Zumino-Witten and fermion models in noncommutative space
• Non Abelian Bosonization in Two and Three Dimensions
• Anomaly and Nonplanar Diagrams in Noncommutative Gauge Theories
• Some properties of the integrable noncommutative sine-Gordon system
• Ultraviolet Property of Noncommutative Wess-Zumino-Witten Model
• The Wess-Zumino-Witten term in non-commutative two-dimensional fermion models
• Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models
• The Faddeev-Jackiw Approach and the Conformal Affine sl(2) Toda Model Coupled to Matter Field
• From Noncommutative Bosonization to S-Duality
• Noether and topological currents equivalence and soliton/particle correspondence in affine $sl(2{)}^{(1)}$ Toda theory coupled to matter
• Chiral anomalies in noncommutative gauge theories
• The covariant form of the gauge anomaly on noncommutative R2n
• Higher Grading Conformal Affine Toda Teory and (Generalized) Sine-Gordon/Massive Thirring Duality
• Affine Toda model coupled to matter and the string tension in QCD${}_2$
• Generalized sine-Gordon/massive Thirring models and soliton/particle correspondences
• UV/IR Mixing and Anomalies in Noncommutative Gauge Theories
• Non-commutative solitons and strong-weak duality
• On Double Gauging of U(1) Symmetry on Noncommutative Space
• Bosonization and generalized Mandelstam soliton operators

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