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

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.

12 pages, 5 figures, minor changes, a version to be published in Physical Review D. arXiv admin note: text overlap with arXiv:1409.1599

References in corpus (3)

• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• Wilson loop and magnetic monopole through a non-Abelian Stokes theorem
• Magnetic monopoles and center vortices as gauge-invariant topological defects simultaneously responsible for confinement

Cited by in corpus (5)

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• Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field
• Gauge gravity vacuum in constraintless Clairaut-type formalism
• How to extract the dominant part of the Wilson loop average in higher representations
• S-duality and loop operators in canonical formalism