Non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation and its implication to quark confinement

TL;DR

This paper presents a gauge-independent approach to defining magnetic monopoles in SU(N) Yang-Mills theory, using a new form of the non-Abelian Stokes theorem to analyze quark confinement across different representations.

Contribution

It provides an explicit proof of the Diakonov-Petrov non-Abelian Stokes theorem for arbitrary representations, enabling gauge-invariant extraction of magnetic monopole effects related to quark confinement.

Findings

Derived a new gauge-invariant form of the non-Abelian Stokes theorem.

Defined magnetic monopoles in a gauge-independent manner.

Linked magnetic monopoles to quark confinement in various representations.

Abstract

We give a gauge-independent definition of magnetic monopoles in the $SU(N)$ Yang-Mills theory through the Wilson loop operator. For this purpose, we give an explicit proof of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of the $SU(N)$ gauge group to derive a new form for the non-Abelian Stokes theorem. The new form is used to extract the magnetic-monopole contribution to the Wilson loop operator in a gauge-invariant way, which enables us to discuss confinement of quarks in any representation from the viewpoint of the dual superconductor vacuum.