Abstract
We discuss Bogomol'nyi equations for general gauge theories (depending on the two Maxwell invariants F μν F μν and F ̃ μνF μν ) 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.
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