From Noncommutative Bosonization to S-Duality

Details From Noncommutative Bosonization to S-Duality From Noncommutative Bosonization to S-Duality

2000-05-07

arxiv.org/abs/hep-th/0005059v1

JHEP 0007 (2000) 030

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, harvmac

Scientific paper

10.1088/1126-6708/2000/07/030

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_\theta^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_\theta^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.

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