Noncommutative Wess-Zumino-Witten actions and their Seiberg-Witten invariance

TL;DR

This paper investigates the noncommutative Wess-Zumino-Witten model in two dimensions, demonstrating its invariance under Seiberg-Witten transformations even in nonchiral cases, with implications for bosonization.

Contribution

It proves Seiberg-Witten invariance of the noncommutative Wess-Zumino-Witten model for both critical and noncritical cases, including nonchiral scenarios.

Findings

Model remains invariant under Seiberg-Witten transformations.

Pure Wess-Zumino term is a singular case where invariance fails.

Results have potential implications for bosonization theories.

Abstract

We analyze the noncommutative two-dimensional Wess-Zumino-Witten model and its properties under Seiberg-Witten transformations in the operator formulation. We prove that the model is invariant under such transformations even for the noncritical (non chiral) case, in which the coefficients of the kinetic and Wess-Zumino terms are not related. The pure Wess-Zumino term represents a singular case in which this transformation fails to reach a commutative limit. We also discuss potential implications of this result for bosonization.