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From Noncommutative Bosonization to S-Duality

Carlos Nunez·Kasper Olsen·Ricardo Schiappa
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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.

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Carlos Nunez, Kasper Olsen, Ricardo Schiappa. 2000-05-07. From Noncommutative Bosonization to S-Duality. https://doi.org/10.1088/1126-6708%2F2000%2F07%2F030

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