From Noncommutative Bosonization to S-Duality

Abstract

We extend standard path-integral techniques of bosonization and duality to the setting of noncommutative geometry. We start by constructing the bosonization prescription for a free Dirac fermion living in the noncommutative plane R_θ^2. We show that in this abelian situation the fermion theory is dual to a noncommutative Wess-Zumino-Witten model. The non-abelian situation is also constructed along very similar lines. We apply the techniques derived to the massive Thirring model on noncommutative R_θ^2 and show that it is dualized to a noncommutative WZW model plus a noncommutative cosine potential (like in the noncommutative Sine-Gordon model). The coupling constants in the fermionic and bosonic models are related via strong-weak coupling duality. This is thus an explicit construction of S-duality in a noncommutative field theory.

15 pages, harvmac

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• Gauged Noncommutative Wess-Zumino-Witten Models
• Bosonized noncommutative bi-fundamental fermion and S-duality
• Ultraviolet properties of noncommutative non-linear sigma-models in two dimensions
• 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
• Duality and bosonization in Schwinger-Keldysh formulation
• Noncommutative Sugawara Construction
• Axial Gauged Noncommutative U(2)/U(1) Wess-Zumino-Witten Model
• Deformed Kac-Moody Algebra and Noncommutative Fermi Theory in Two-Dimensions