Uniqueness of Bogomolʹnyi equations and Born-Infeld like supersymmetric theories

We discuss Bogomolʹnyi equations for general gauge theories (depending on the two Maxwell invariants FμνFμν and F̃μνFμν) coupled to Higgs scalars. By analysing their supersymmetric extension, we explicitly show why the resulting BPS structure is insensitive to the particular form of the gauge Lagrangian: Maxwell, Born-Infeld or more complicated non-polynomial Lagrangians all satisfy the same Bogomolʹnyi equations and bounds which are dictated by the underlying supersymmetry algebra.