From Noncommutative Bosonization to S-Duality

TL;DR

This paper develops noncommutative bosonization and duality techniques, establishing an explicit S-duality between fermionic and bosonic models in noncommutative geometry, including the Thirring and WZW models.

Contribution

It extends bosonization and duality methods to noncommutative spaces, explicitly constructing S-duality in noncommutative field theories.

Findings

Fermion theory on noncommutative plane is dual to a noncommutative WZW model.

Massive Thirring model is dual to a noncommutative WZW model with a cosine potential.

Coupling constants are related via strong-weak duality, demonstrating 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_\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.