Parent action approach for the duality between non-Abelian self-dual and Yang–Mills–Chern–Simons models

It has been argued by some authors that the parent action approach cannot be used in order to establish the duality between the 2+1 Abelian and non-Abelian Self-Dual (SD) and Yang–Mills–Chern–Simons (YMCS) models for all the coupling regimes. We propose here an alternative (perturbative) point of view, and show that this equivalence can be achieved with the parent action approach.