Wess-Zumino-Witten and fermion models in noncommutative space

Abstract

We analyze the connection between Wess-Zumino-Witten and free fermion models in two-dimensional noncommutative space. Starting from the computation of the determinant of the Dirac operator in a gauge field background, we derive the corresponding bosonization recipe studying, as an example, bosonization of the U(N) Thirring model. Concerning the properties of the noncommutative Wess-Zumino-Witten model, we construct an orbit-preserving transformation that maps the standard commutative WZW action into the noncommutative one.

27 pages, 1 figure. LaTex file

References in corpus (8)

• String Theory and Noncommutative Geometry
• Space/Time Non-Commutativity and Causality
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• Comments on Noncommutative Perturbative Dynamics
• Chiral Gauge Anomalies on Noncommutative R^4
• Induced Chern-Simons and WZW action in Noncommutative Spacetime
• The Wess-Zumino-Witten term in non-commutative two-dimensional fermion models
• From Noncommutative Bosonization to S-Duality

Cited by in corpus (30)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Integrable Noncommutative Sine-Gordon Model
• Noncommutative Chiral Gauge Theories on the Lattice with Manifest Star-Gauge Invariance
• Seiberg-Witten maps from the point of view of consistent deformations of gauge theories
• Chiral Anomaly on Fuzzy 2-Sphere
• Some properties of the integrable noncommutative sine-Gordon system
• Heat kernel, effective action and anomalies in noncommutative theories
• The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level
• Chiral anomalies in noncommutative gauge theories
• Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
• Duality between Noncommutative Yang-Mills-Chern-Simons and Non-Abelian Self-Dual Models
• Gauged Noncommutative Wess-Zumino-Witten Models
• Bosonized noncommutative bi-fundamental fermion and S-duality
• Three lectures on noncommutative field theories
• Computing noncommutative Chern-Simons theory radiative corrections on the back of an envelope
• On the mass spectrum of noncommutative Schwinger model in Euclidean ${\mathbb{R}}^2$ space
• On the energy-momentum tensor in Moyal space
• Bosonization in higher dimensions via noncommutative field theory
• Anomalies in Noncommutative Dipole Field Theories
• Non-commutative solitons and strong-weak duality
• Ultraviolet properties of noncommutative non-linear sigma-models in two dimensions
• The Seiberg-Witten Map for Noncommutative Gauge Theories
• Aspects of perturbative quantum field theory on non-commutative spaces
• Non-commutative Duality: High Spin Fields and $C{P}^1$ Model with Hopf Term
• Noncommutative fermions and Morita equivalence
• Twisted Conformal Field Theories and Morita equivalence
• Noncommutative Wess-Zumino-Witten actions and their Seiberg-Witten invariance
• Deformed Kac-Moody Algebra and Noncommutative Fermi Theory in Two-Dimensions
• Axial Gauged Noncommutative U(2)/U(1) Wess-Zumino-Witten Model