A Topological Bound for Electroweak Vortices from Supersymmetry

We study the connection between N=2 supersymmetry and a topological bound in a two-Higgs-doublet system having an $SU(2)\times U(1)_Y\times U(1)_{Y'}$ gauge group. We derive Bogomol'nyi equations from supersymmetry considerations showing that they hold provided certain conditions on the coupling constants, which are a consequence of the huge symmetry of the theory, are satisfied.