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