Supersymmetric Dirac-Born-Infeld action with self-dual mass term

We introduce a Dirac-Bom-Infeld action to a self-dual N = 1 supersymmetric vector multiplet in three dimensions. This action is based on the supersymmetric generalized self-duality in odd dimensions developed originally by Townsend, Pilch and van Nieuwenhuizen. Even though such a self-duality had been supposed to be very difficult to generalize to a supersymmetrically interacting system, we show that the Dirac-Bom-Infeld action is actually compatible with supersymmetry and self-duality in three dimensions, even though the original self-duality receives corrections by the Dirac-Bom-Infeld action. The interactions can be further generalized to arbitrary (non)polynomial interactions. As a by-product, we also show that a third-rank field strength leads to a more natural formulation of self-duality in 3D. We also show an interesting role played by the third-rank field strength leading to supersymmetry breaking, in addition to accommodating a Chem-Simons form.