Topology of Center Vortices

TL;DR

This paper investigates the topological properties of idealized center vortices in gauge theories, revealing that the topological charge of vortex loops can be described by their writhing number changes over time.

Contribution

It introduces a gauge-invariant definition of center vortices as closed flux surfaces and links their topological charge to the dynamics of their writhing number.

Findings

Topological charge is expressed by temporal changes in writhing number.

Center vortices are modeled as closed flux surfaces contributing to Wilson loops.

The study provides a mathematical framework for vortex topology in gauge theories.

Abstract

In this talk I study the topology of mathematically idealised center vortices, defined in a gauge invariant way as closed (infinitely thin) flux surfaces (in D=4 dimensions) which contribute the $n^{th}$ power of a non-trivial center element to Wilson loops when they are n-foldly linked to the latter. In ordinary 3-space generic center vortices represent closed magnetic flux loops which evolve in time. I show that the topological charge of such a time-dependent vortex loop can be entirely expressed by the temporal changes of its writhing number.