Duality between non-commutative Yang–Mills–Chern–Simons and non-Abelian self-dual models

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 non-commutative Yang–Mills–Chern–Simons theory and the non-commutative, 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.