Classical dynamics of strings and branes, with application to vortons

TL;DR

This paper provides an introduction to classical brane dynamics using geometric methods and applies this framework to analyze the stability of vorton states in cosmic string loops within four-dimensional spacetime.

Contribution

It offers a systematic geometric approach to brane dynamics and applies it specifically to the stability analysis of vortons in cosmic strings.

Findings

Geometric formulation of brane dynamics emphasizing the second fundamental tensor.

Application of the framework to vorton stability in 4D spacetime.

Insights into conditions for vorton equilibrium stability.

Abstract

These notes offer an introductory overview of the essentials of classical brane dynamics in a space-time background of arbitrary dimension, using a systematic geometric treatment emphasising the role of the second fundamental tensor and its trace, the curvature vector $K^\mu$. This approach is applied to the problem of stability of vorton equilibrium states of cosmic string loops in an ordinary 4-dimensional background.