Analytical BPS Maxwell-Higgs vortices

TL;DR

This paper develops a method to find exact analytical vortex solutions in generalized Maxwell-Higgs models, expanding understanding of topological solitons with properties similar to classical solutions.

Contribution

It introduces a prescription for analytical BPS vortex solutions in generalized models, linking functions and potential, and provides exact solutions under specific conditions.

Findings

Analytical vortex solutions are obtained for generalized Maxwell-Higgs models.

Solutions exhibit properties similar to classical Abrikosov-Nielsen-Olesen vortices.

The models support well-behaved, localized energy configurations.

Abstract

We have established a prescription for the calculation of analytical vortex solutions in the context of generalized Maxwell-Higgs models whose overall dynamics is controlled by two positive functions of the scalar field. We have also determined a natural constraint between these functions and the Higgs potential allowing the existence of axially symmetric Bogomol'nyi-Prasad-Sommerfield (BPS) solutions possessing finite energy. Furthermore, when the generalizing functions are chosen suitably, the nonstandard BPS equations can be solved exactly. We have studied some examples, comparing them with the usual Abrikosov-Nielsen-Olesen (ANO) solution. The overall conclusion is that the analytical self-dual vortices are well-behaved in all relevant sectors, strongly supporting the generalized models they belong themselves. In particular, our results mimic well-known properties of the usual (numerical) configurations, as localized energy density, while contributing to the understanding of topological solitons and their description by means of analytical methods.