Self-Dual Cosmic Strings and Gravitating Vortices in Gauged Sigma Models

TL;DR

This paper explores self-dual cosmic string solutions in gauged sigma models with Maxwell or Chern-Simons kinetic terms, analyzing their properties and differences, including the emergence of spinning vortices in the Chern-Simons case.

Contribution

It derives self-duality conditions for gauged sigma models with general target spaces and compares solutions in Maxwell and Chern-Simons models, highlighting new features like spinning vortices.

Findings

Analytical and numerical solutions for O(3) models

Classification of solutions by flux and topological charge

Identification of spinning vortices in Chern-Simons models

Abstract

Cosmic strings are considered in two types of gauged sigma models, which generalize the gravitating Abelian Higgs model. The two models differ by whether the U(1) kinetic term is of the Maxwell or Chern-Simons form. We obtain the self-duality conditions for a general two-dimensional target space defined in terms of field dependent "dielectric functions". In particular, we analyze analytically and numerically the equations for the case of O(3) models (two-sphere as target space), and find cosmic string solutions of several kinds as well as gravitating vortices. We classify the solutions by their flux and topological charge. We note an interesting connection between the Maxwell and Chern-Simons type models, which is responsible for simple relations between the self-dual solutions of both types. There is however a significant difference between the two systems, in that only the Chern-Simons type sigma model gives rise to spinning cosmic vortices.