Classical solutions of the Gravitating Abelian Higgs Model

TL;DR

This paper investigates classical solutions in the gravitating Abelian-Higgs model, exploring vortex configurations with various winding numbers and phases, including self-dual cases, revealing detailed properties of these solutions.

Contribution

It provides new insights into the properties and existence of vortex solutions in the gravitating Abelian-Higgs model, including for higher winding numbers and different phase regimes.

Findings

Vortex solutions exist in both attractive and repulsive phases.

Solutions are constructed for winding number N=2.

Self-dual equations mark the boundary between phases.

Abstract

We consider the classical equations of the gravitating Abelian-Higgs model in an axially symmetric ansatz. More properties of the solutions of these equations (the Melvin and the sting branches) are presented. These solutions are also constructed for winding numbers N=2. It is shown that these vortices exist in attractive and repulsive phases, separated by the value of the Higgs coupling constant parameter leading to self-dual equations.