Center Vortices in Continuum Yang-Mills Theory

TL;DR

This paper explores the properties of center vortices in continuum Yang-Mills theory, deriving their gauge potential from lattice theory and linking their topological features to magnetic monopoles and self-intersection numbers.

Contribution

It provides a continuum formulation of center vortices, connecting lattice results to continuum gauge fixing and topological invariants, and clarifies the role of magnetic monopoles.

Findings

Pontryagin index equals vortex self-intersection number

Self-intersection number vanishes unless magnetic monopoles are present

Magnetic monopoles induce non-orientability in vortex sheets

Abstract

The properties of center vortices are discussed within continuum Yang-Mills theory. By starting from the lattice theory and carefully performing the continuum limit the gauge potential of center vortices is obtained and the continuum analog of the maximal center gauge fixing is extracted. It is shown, that the Pontryagin index of center vortices is given by their self-intersection number, which vanishes unless the center vortices host magnetic monpoles, which make the vortex sheets non-oriented.