A Method for BPS Equations of Vortices

Abstract

We develop a new method for obtaining the BPS equations of static vortices motivated by the results of the \textit{On-Shell} method on the standard Maxwell-Higgs model and its Born-Infeld-Higgs model~\cite{Atmaja:2014fha}. Our method relies on the existence of what we shall call an energy function, $Q$, which is a mere function of the (effective) fields. The total energy of BPS vortices, $E_{BPS}$, are simply given by a difference between the boundaries value of $Q$ at $r\to \infty$ and at $r=0$, $E_{BPS}=Q(r\to \infty )-Q(r=0)$. Imposing a condition that these (effective) fields are independent, we may define a BPS Lagrangian, ${\mathcal{L}}_{BPS}$, derived by taking integral of differential $Q$, ${\mathcal{L}}_{BPS}=-\int dQ$. Matching the Lagrangian ${\mathcal{L}}_{BPS}$ with the corresponding effective Lagrangian, we can extract several equations. Solving these equations yields the desired BPS equations and, in some cases, also constraint equations. With our method, the various known BPS equations of vortices are derived in a relatively simple procedure.

17 pages. Comments are welcomed

References in corpus (3)

• Generalized Global Defect Solutions
• Bogomol'nyi Equations for Vortices in Born-Infeld-Higgs Systems
• On Bogomol'nyi Equations of Classical Solutions

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• Vortices in a generalized Maxwell-Higgs model with visible and hidden sectors
• On Bogomolny equations in generalized gauged baby BPS Skyrme models
• Vortices in vacuumless systems
• Bogomol'nyi equations for Dirac-Born-Infeld cosmic string
• Topologically Stable BPS and Non-BPS States in Supersymmetric $\mathcal{N}=2$ Baby-Skyrme Model
• Vortices in Maxwell-Higgs models with a global factor
• First order framework for gauge k-vortices
• Radial Stabilization of Magnetic Skyrmions Under Strong External Magnetic Field