  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.
