Gauge invariance and duality in the non-commutative plane

Abstract

We show that the duality between the self-dual and Maxwell–Chern–Simons theories in 2+1 dimensions survives when the spacetime becomes non-commutative. 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.