Center Projection Vortices in Continuum Yang-Mills Theory

TL;DR

This paper develops a continuum version of the maximal center gauge to study center vortices in Yang-Mills theory, linking lattice methods to continuum physics and exploring vortex contributions to topological charge.

Contribution

It introduces a continuum analogue of the maximal center gauge and proposes an effective vortex theory, enhancing understanding of vortex physics in continuum Yang-Mills theory.

Findings

Constructed a continuum version of the maximal center gauge.

Linked vortex configurations to the Pontryagin index via self-intersections.

Provided insights into the topological role of non-oriented vortex surfaces.

Abstract

The maximal center gauge, combined with center projection, is a means to associate Yang-Mills lattice gauge configurations with closed center vortex world-surfaces. This technique allows to study center vortex physics in lattice gauge experiments. In the present work, the continuum analogue of the maximal center gauge is constructed. This sheds new light on the meaning of the procedure on the lattice and leads to a sketch of an effective vortex theory in the continuum. Furthermore, the manner in which center vortex configurations generate the Pontryagin index is investigated. The Pontryagin index is built up from self-intersections of the vortex world-surfaces, where it is crucial that the surfaces be globally non-oriented.