Chern-Simons-Higgs Theory with Visible and Hidden Sectors and its ${\cal N}=2$ SUSY Extension

TL;DR

This paper investigates vortex solutions in Abelian Chern-Simons-Higgs theories with visible and hidden sectors, exploring gauge mixing effects, supersymmetric extensions, and numerical solutions of Bogomolnyi equations.

Contribution

It introduces an ${ m N}=2$ supersymmetric extension with Higgs portal mixing, enabling Bogomolnyi equations and vortex solutions in coupled sectors.

Findings

No Bogomolny equations without supersymmetry in gauge-mixed case

Supersymmetric extension yields Bogomolnyi equations

Numerical vortex solutions found in supersymmetric case

Abstract

We study vortex solutions in Abelian Chern-Simons-Higgs theories with visible and hidden sectors. We first consider the case in which the two sectors are connected through a BF-like gauge mixing term with no explicit interaction between the the two scalars. Since first order Bogomolny equations do not exist in this case, we derive the second order field equations. We then proceed to an ${\cal N}=2$ supersymmetric extension including a Higgs portal mixing among the visible and hidden charged scalars. As expected, Bogomolnyi equations do exist in this case and we study their string-like solutions numerically.