Gauge Invariance and Duality in the Noncommutative Plane

TL;DR

This paper demonstrates that the duality between self-dual and Maxwell-Chern-Simons theories persists in a noncommutative space-time, emphasizing the role of the Seiberg-Witten map and gauge invariance.

Contribution

It extends the duality between these theories to noncommutative geometry using the Seiberg-Witten map and explores the gauge properties via the Stuckelberg formalism.

Findings

Duality survives in noncommutative space-time.

Seiberg-Witten map is essential for analysis.

Different transformations under the map for gauge variant/invariant models.

Abstract

We show that the duality between the self-dual and Maxwell-Chern-Simons theories in 2+1-dimensions survives when the space-time becomes noncommutative. Existence of the Seiberg-Witten map is crucial in the present analysis. It should be noted that the above models, being manifestly gauge variant and invariant respectively, transform differently under the Seiberg-Witten map. We also discuss this duality in the Stuckelberg formalism where the self-dual model is elevated to a gauge theory. The "`master"' lagrangian approach has been followed throughout.