Two-field Born-Infeld with diverse dualities

We elaborate on how to build, in a systematic fashion, two-field Abelian extensions of the Born-Infeld Lagrangian. These models realize the non-trivial duality groups that are allowed in this case, namely U(2), SU(2) and U(1)×U(1). For each class, we also construct an explicit example. They all involve an overall square root and reduce to the Born-Infeld model if the two fields are identified, but differ in quartic and higher interactions. The U(1)×U(1) and SU(2) examples recover some recent results obtained with different techniques, and we show that the U(1)×U(1) model admits an N=1 supersymmetric completion. The U(2) example includes some unusual terms that are not analytic at the origin of field space.