Topological charge of Center Vortices

TL;DR

This paper explores the topological charge of center vortices by relating it to self-intersection numbers of vortex surfaces in 4D and the writhing number changes of vortex loops in 3D, providing a geometric perspective.

Contribution

It introduces a novel geometric framework connecting topological charge to self-intersection and writhing numbers of vortices in different dimensions.

Findings

Topological charge linked to self-intersection number of vortex surfaces.

Topological charge related to temporal changes in vortex loop writhing.

Provides a geometric interpretation of vortex topological properties.

Abstract

The topological charge of center vortices is discussed in terms of the self-intersection number of the closed vortex surfaces in 4-dimensional Euclidian space-time and in terms of the temporal changes of the writhing number of the time-dependent vortex loops in 3-dimensional space.