A Unified Approach To Find The Generalized Maxwell-Chern-Simons-Higgs BPS Vortices and Their Properties

TL;DR

This paper introduces a unified framework to derive all BPS vortex solutions in the generalized Maxwell-Chern-Simons-Higgs model using a single set of equations, enabling classification and analysis of vortex properties.

Contribution

It presents a novel unified approach to find BPS vortices in the generalized MCSH model via a single system of equations derived from the BPS Lagrangian method.

Findings

All vortex solutions can be obtained from a single equation system.

Known spherically symmetric vortices are special cases of the generalized equations.

Vortices exhibit similar behaviors under parameter variations.

Abstract

In this work, we propose that all BPS vortex solutions within the generalized Maxwell-Chern-Simons-Higgs (MCSH) model can be found from a single system of equations. This set of equations is derived using the BPS Lagrangian method, which is a more robust generalization of Bogomolnyi's trick. We show that the known spherically symmetric BPS vortices can be reproduced as certain limits of Bogomolnyi equations in the generalized MCSH Model. This provides us with a possible classification system using the auxiliary functions in the BPS Lagrangian. Furthermore, we also study the properties of each known vortex through the numerical approach where we found that all of the vortices behave similarly under variations of their free parameters and a system of well-separated MCSH vortices saturates the BPS bound.