Vortices and cosmic strings in a generalized Born-Infeld model

TL;DR

This paper investigates topological solitons, specifically vortices and cosmic strings, within a generalized Born-Infeld-Higgs model, establishing their existence, decay properties, and energy quantization, including coupling with Einstein's equations for cosmic strings.

Contribution

It demonstrates the existence of vortex and cosmic string solutions in a generalized Born-Infeld-Higgs framework, including coupling with gravity and quantized energy depending on topological charge.

Findings

Existence of planar vortex solutions in the model.

Existence of cosmic string solutions on noncompact Riemann surfaces.

Energy quantization depending on vortex and string numbers.

Abstract

In this paper, we consider two types of topological solitons in a generalized Born-Infeld-Higgs model. We explore the self-dual structure of the model and prove the existence of planar vortex solutions. Furthermore, we couple the system with the Einstein equations and study the cosmic strings problem over $\mathbb R^{1,1}\times S$, where $S$ is a Riemann surface. We prove the existence of cosmic string solutions when $S$ is noncompact. We also discuss the decay estimates for vortices and cosmic strings at infinity and show that the minimal energy is quantized and depends on the number of vortices and strings, respectively.