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arXiv · 1509.04891

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

Ryutaro Matsudo·Kei-Ichi Kondo
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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.

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Ryutaro Matsudo, Kei-Ichi Kondo. 2016-01-03. Non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation and its implication to quark confinement. https://doi.org/10.1103/physrevd.92.125038

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