Wess-Zumino-Witten and fermion models in noncommutative space

TL;DR

This paper explores the relationship between Wess-Zumino-Witten and fermion models in two-dimensional noncommutative space, deriving bosonization techniques and transformations connecting commutative and noncommutative models.

Contribution

It introduces a method to derive bosonization in noncommutative space and constructs a transformation linking commutative and noncommutative WZW models.

Findings

Derived bosonization recipe for noncommutative models

Constructed an orbit-preserving transformation between models

Analyzed properties of noncommutative WZW model

Abstract

We analyze the connection between Wess-Zumino-Witten and free fermion models in two-dimensional noncommutative space. Starting from the computation of the determinant of the Dirac operator in a gauge field background, we derive the corresponding bosonization recipe studying, as an example, bosonization of the U(N) Thirring model. Concerning the properties of the noncommutative Wess-Zumino-Witten model, we construct an orbit-preserving transformation that maps the standard commutative WZW action into the noncommutative one.