Duality in Noncommutative Topologically Massive Gauge Field Theory Revisited

TL;DR

This paper explores dualities in noncommutative gauge theories, deriving new dual models at first and second order in the noncommutative parameter, and discusses implications for bosonization in three dimensions.

Contribution

It introduces a master action for noncommutative Maxwell-Chern-Simons theory and explicitly constructs dual theories at first and second order, revealing local dual models unlike non-Abelian cases.

Findings

First-order dual theory generalizes the commutative Self-Dual model with a noncommutative Chern-Simons term.

Second-order calculations yield a new, simple local dual theory involving ordinary fields.

Results support the possibility of noncommutative bosonization only at first non-trivial order.

Abstract

We introduce a master action in noncommutative space, out of which we obtain the action of the noncommutative Maxwell-Chern-Simons theory. Then, we look for the corresponding dual theory at both first and second orders in the noncommutative parameter. At the first order, the dual theory happens to be, precisely, the action obtained from the usual commutative Self-Dual model by generalizing the Chern-Simons term to its noncommutative version, including a cubic term. Since this resulting theory is also equivalent to the noncommutative massive Thirring model in the large fermion mass limit, we remove, as a byproduct, the obstacles arising in the generalization to noncommutative space, and to the first nontrivial order in the noncommutative parameter, of the bosonization in three dimensions. Then, performing calculations at the second order in the noncommutative parameter, we explicitly compute a new dual theory which differs from the noncommutative Self-Dual model, and further, differs also from other previous results, and involves a very simple expression in terms of ordinary fields. In addition, a remarkable feature of our results is that the dual theory is local, unlike what happens in the non-Abelian, but commutative case. We also conclude that the generalization to noncommutative space of bosonization in three dimensions is possible only when considering the first non-trivial corrections over ordinary space.