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

We discuss Bogomol'nyi equations for general gauge theories (depending on t he two Maxwell invariants (FFmu nu)-F-mu nu and (F) over tilde(mu nu)F(mu n u)) coupled to Higgs scalars. By analysing their supersymmetric extension, we explicitly show why the resulting BPS structure is insensitive to the pa rticular form of the gauge Lagrangian: Maxwell, Born-Infeld or more complic ated non-polynomial Lagrangians all satisfy the same Bogomol'nyi equations and bounds which are dictated by the underlying supersymmetry algebra. (C) 1998 Elsevier Science B.V. All rights reserved.