From Noncommutative Bosonization to S-Duality

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 Rθ. 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 Rθ 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.