Noncommutative Maxwell-Chern-Simons theory in three dimensions and its dual

TL;DR

This paper explores the noncommutative Maxwell-Chern-Simons theory in three dimensions, revealing ambiguities in the Seiberg-Witten map, deriving a dual theory via a master action, and showing the breakdown of classical equivalence in the noncommutative context.

Contribution

It introduces a novel approach to formulating the dual of noncommutative Maxwell-Chern-Simons theory and analyzes the impact of noncommutativity on known dualities.

Findings

Seiberg-Witten map ambiguity due to dimensional coupling

Derived dual theory from a master action approach

Classical duality between Maxwell-Chern-Simons and self-dual models does not hold in noncommutative space

Abstract

We consider the Maxwell-Chern-Simons theory in noncommutative three dimensional space-time. We show that the Seiberg-Witten map is ambiguous due to the dimensional coupling constant. To get the dual theory we start from a master action obtained by promoting the global shift invariance to a local one. We also obtain the mapping between the observables of the two equivalent theories. We show that the equivalence between the Maxwell-Chern-Simons theory and the self-dual model in commutative space-time does not survive in the non-commutative setting.