Duality in non-linear BF models: equivalence between self-dual and topologically massive Born–Infeld BF models

We study the dual equivalence between the non-linear generalization of the self-dual (NSD_BF) and the topologically massive BF models with particular emphasis on the non-linear electrodynamics proposed by Born and Infeld. This is done through a dynamical gauge embedding of the non-linear self-dual model yielding to a gauge invariant and dynamically equivalent theory. We clearly show that non-polinomial NSD_BF models can be map, through a properly defined duality transformation into TM_BF actions. The general result obtained is then particularized for a number of examples, including the Born–Infeld-BF (BIBF) model that has experienced a revival in the recent literature.