Topology of Center Vortices

TL;DR

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

Contribution

It introduces a gauge-invariant framework for understanding the topology of idealized center vortices and relates topological charge to the temporal evolution of vortex writhing.

Findings

Topological charge of vortex loops is expressed by changes in writhing number.

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

Topological properties are linked to the evolution of vortex configurations over time.

Abstract

The topology of center vortices is studied. For this purpose it is sufficient to consider mathematically idealised 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.