Supersymmetric Electroweak Cosmic Strings

TL;DR

This paper explores the link between N=2 supersymmetry and topological bounds in a two-Higgs-doublet model with an extended gauge group, deriving Bogomol'nyi equations and analyzing electroweak cosmic string solutions.

Contribution

It derives Bogomol'nyi equations from supersymmetry in a complex gauge theory and studies electroweak cosmic string solutions that preserve half of the supersymmetries.

Findings

Derived conditions for Bogomol'nyi equations from supersymmetry.

Found solutions interpreted as electroweak cosmic strings breaking half the supersymmetries.

Analyzed special limiting cases relevant to recent literature.

Abstract

We study the connection between $N=2$ supersymmetry and a topological bound in a two-Higgs-doublet system with an $SU(2)\times U(1)_Y\times U(1)_{Y^{\prime}}$ 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.