Duality between Noncommutative Yang-Mills-Chern-Simons and Non-Abelian Self-Dual Models

TL;DR

This paper demonstrates the equivalence between noncommutative Yang-Mills-Chern-Simons theory and non-Abelian Self-Dual models using perturbative methods, Moyal star-product, and Seiberg-Witten map, up to fourth order in fields.

Contribution

It establishes a duality between two noncommutative gauge theories through a perturbative approach and explores two different formalisms, expanding understanding of their relationship.

Findings

Proves equivalence up to fourth order in fields.

Uses both Moyal star-product and Seiberg-Witten map.

Valid for the full range of the coupling constant.

Abstract

By introducing an appropriate parent action and considering a perturbative approach, we establish, up to fourth order terms in the field and for the full range of the coupling constant, the equivalence between the noncommutative Yang-Mills-Chern-Simons theory and the noncommutative, non-Abelian Self-Dual model. In doing this, we consider two different approaches by using both the Moyal star-product and the Seiberg-Witten map.