On the dual equivalence of the Born-Infeld-Chern-Simons model coupled to dynamical U(1) charged matter

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We study the equivalence between a nonlinear self-dual model (NSD) with the Born-Infeld-Chern-Simons (BICS) models using an iterative gauge embedding procedure that produces the duality mapping, including the case where the NSD model is minimally coupled to dynamical, U(1) charged fermionic matter. The duality mapping introduces a current-current interaction term while at the same time the minimal coupling of the original nonlinear self-dual model is replaced by a non-minimal magnetic like coupling in the BICS side.