Non-linear Electrodynamics from Massive Gravity

As a counterpart to the four-fermion interaction, which describes massive vector exchange at low energies, we investigate the low energy effective action of photons under exchange of a massive graviton. We show how integrating out a massive graviton leads to the most general duality-invariant vector interactions in 4D or, vice versa, how any such interactions have a natural interpretation within massive gravity. Moreover, we demonstrate how the special case of Born-Infeld theory arises from arguably the simplest graviton potential within ghost-free dRGT massive gravity.