A Topological Bound for Electroweak Vortices from Supersymmetry

TL;DR

This paper explores how N=2 supersymmetry imposes a topological bound on electroweak vortices within a two-Higgs-doublet model, deriving Bogomol'nyi equations under specific symmetry conditions.

Contribution

It establishes a connection between supersymmetry and topological bounds in electroweak vortex configurations, deriving Bogomol'nyi equations from symmetry considerations.

Findings

Derivation of Bogomol'nyi equations from supersymmetry

Identification of conditions on coupling constants

Link between symmetry and topological bounds

Abstract

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.