A gauge-invariant object in non-Abelian gauge theory

TL;DR

This paper introduces a gauge-invariant nonlocal object in non-Abelian gauge theory using Wilson loops, revealing monopole-like features relevant to color confinement and lattice studies.

Contribution

It defines a new gauge-invariant object via Wilson loops in non-Abelian theories, linking monopole structures to confinement phenomena.

Findings

The object exhibits monopole-like behavior in gluon fields.

It shares features with 't Hooft-Polyakov monopoles.

Potential applications in lattice gauge theory.

Abstract

We propose a nonlocal definition of a gauge-invariant object in terms of the Wilson loop operator in a non--Abelian gauge theory. The trajectory is a closed curve defined by an (untraced) Wilson loop which takes its value in the center of the color group. We show that definition shares basic features with the gauge-dependent 't Hooft construction of Abelian monopoles in Yang-Mills theories. The chromoelectric components of the gluon field have a hedgehog-like behavior in the vicinity of the object. This feature is dual to the structure of the 't Hooft-Polyakov monopoles which possesses a hedgehog in the magnetic sector. A relation to color confinement and lattice implementation of the proposed construction are discussed.