Wilson loop and magnetic monopole through a non-Abelian Stokes theorem

Journal Article · Tue Apr 15 04:00:00 EDT 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.77.085029· OSTI ID:21250064

Kondo, Kei-Ichi ^[1]

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1. Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522 (Japan)

I show that the Wilson loop operator for the SU(N) Yang-Mills gauge connection is exactly rewritten in terms of conserved gauge-invariant magnetic and electric currents through a non-Abelian Stokes theorem of the Diakonov-Petrov type. Here the magnetic current originates from the magnetic monopole derived in the gauge-invariant way from the pure Yang-Mills theory even in the absence of the Higgs scalar field, in sharp contrast to the 't Hooft-Polyakov magnetic monopole in the Georgi-Glashow gauge-Higgs model. The resulting representation indicates that the Wilson loop operator in fundamental representations can be a probe for a single magnetic monopole irrespective of N in SU(N) Yang-Mills theory, against the conventional wisdom. Moreover, I show that the quantization condition for the magnetic charge follows from the fact that the non-Abelian Stokes theorem does not depend on the surface chosen for writing the surface integral. The obtained geometrical and topological representations of the Wilson loop operator have important implications to understanding quark confinement according to the dual superconductor picture.

• OSTI ID: 21250064
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 77; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BAG MODEL
ELECTRIC CURRENTS
GAUGE INVARIANCE
HIGGS MODEL
MAGNETIC MONOPOLES
QUANTIZATION
SCALAR FIELDS
SU GROUPS
SUPERCONDUCTIVITY
SURFACES
WILSON LOOP
YANG-MILLS THEORY