We study the connection between $N=2\mathrm{}$ supersymmetry and a topological bound in a two-Higgs-doublet system with a $\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}\times \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_Y\times \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_{Y^{\prime }}$ gauge group. We derive the 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. Their solutions, which can be interpreted as electroweak cosmic strings breaking one-half of the supersymmetries of the theory, are studied. Certain interesting limiting cases of our model which have recently been considered in the literature are finally analyzed.

• Received 30 April 1996

DOI:https://doi.org/10.1103/PhysRevD.55.3811