On derivation of BPS equations of vortices in K-generalized Abelian-Higgs model

Abstract

A new self-dual equation, or BPS equations, of vortices in the K-generalized Abelian-Higgs Model was derived by exploiting the identity equation of the scalar kinetic terms [1]. Here we develop a method for obtaining these BPS equations by assuming the BPS energy EBPS can be written as an integral over total derivative of energy function Q, which is a function of the effective fields, as such we can define a BPS Lagrangian ℒBPS ∝ −Q′(r), where r is an effective coordinate. Matching this BPS Lagrangian with the corresponding effective Lagrangian, we can extract the resulting BPS equations. We show there are two ways to get the BPS equations of vortices in the K-generalized Abelian-Higgs Model using our method.