Uniqueness of Bogomol'nyi equations and Born-Infeld like supersymmetric theories

We discuss Bogomol'nyi equations for general gauge theories (depending on the two Maxwell invariants $F^{\mu \nu} F_{\mu \nu}$ and $\tilde F^{\mu \nu} F_{\mu \nu}$) 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 Bogomol'nyi equations and bounds which are dictated by the underlying supersymmetry algebra.