On duality of the noncommutative Maxwell-Chern-Simons theory

TL;DR

This paper investigates the duality relationship between noncommutative Maxwell-Chern-Simons theory and noncommutative self-dual theory, revealing that duality holds only with a modified Maxwell term in the noncommutative setting.

Contribution

It demonstrates that the duality between these theories in the noncommutative case requires a modified Maxwell term, unlike the commutative case.

Findings

Duality exists only with a modified Maxwell term in noncommutative theories.

In the commutative case, the Maxwell-Chern-Simons theory maps to self-dual and Chern-Simons theories.

The noncommutative case restricts the duality mapping compared to the commutative case.

Abstract

We study the possibility of establishing the dual equivalence between the noncommutative Maxwell-Chern-Simons theory and the noncommutative self-dual theory. It turns to be that whereas in the commutative case the Maxwell-Chern-Simons theory can be mapped into the sum of the self-dual theory and the Chern-Simons theory, in the noncommutative case such a mapping is possible only for the theory with the modified Maxwell term.