Dual equivalence between self-dual and Maxwell–Chern–Simons models coupled to dynamical U(1) charged matter

We study the equivalence between the self-dual and the Maxwell–Chern–Simons (MCS) models coupled to dynamical, U(1) charged matter, both fermionic and bosonic. This is done through an iterative procedure of gauge embedding that produces the dual mapping of the self-dual vector field theory into a Maxwell–Chern–Simons version. In both cases, to establish this equivalence a current–current interaction term is needed to render the matter sector unchanged. Moreover, the minimal coupling of the original self-dual model is replaced by a non-minimal magnetic like coupling in the MCS side. Unlike the fermionic instance however, in the bosonic example the dual mapping proposed here leads to a Maxwell–Chern–Simons theory immersed in a field dependent medium.