Surface operators and magnetic degrees of freedom in Yang-Mills theories

TL;DR

This paper explores magnetic degrees of freedom in Yang-Mills theories, proposing that surface operators represent Abelian magnetic defects that explain lattice observations like Abelian dominance in confinement.

Contribution

It introduces surface operators as a general solution for magnetic defects in Yang-Mills theories, linking them to Abelian structures and lattice phenomena.

Findings

Surface operators serve as prototypes of magnetic degrees of freedom.

Magnetic defects are Abelian in nature, preserving color conservation.

Lattice observations like Abelian dominance are explained through these defects.

Abstract

Magnetic degrees of freedom are manifested through violations of the Bianchi identities and associated with singular fields. Moreover, these singularities should not induce color non-conservation. We argue that the resolution of the constraint is that the singular fields, or defects are Abelian in nature. Recently proposed surface operators seem to represent a general solution to this constraint and can serve as a prototype of magnetic degrees of freedom. Some basic lattice observations, such as the Abelian dominance of the confining fields, are explained then as consequences of the original non-Abelian invariance.