Vortices in Bogomol'nyi Limit of Einstein Maxwell Higgs Theory with or without External Sources

TL;DR

This paper explores vortex solutions in the Einstein-Maxwell-Higgs theory at the Bogomol'nyi limit, analyzing their properties in curved space with various external sources and geometries.

Contribution

It introduces a dual transformation approach to derive Bogomol'nyi bounds and finds new vortex and vortex-particle solutions in curved spacetime.

Findings

Vortex solutions exist in cylindrical and spherical geometries.

Dual transformation simplifies the analysis of Bogomol'nyi bounds.

Solutions include vortex-particle composites in curved backgrounds.

Abstract

The Abelian Higgs model with or without external particles is considered in curved space. Using the dual transformation, we rewrite the model in terms of dual gauge fields and derive the Bogomol'nyi-type bound. We examine cylindrically symmetric solutions to Einstein equations and the first-order Bogomol'nyi equations, and find vortex solutions and vortex-particle composites which lie on the spatial manifold with global geometry described by a cylinder asymptotically or a two sphere in addition to the well-known cone.