A gauge-invariant object in non-Abelian gauge theory

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We propose a non-local definition of a gauge-invariant object in terms of the Wilson loop operator in a non-Abelian gauge theory. The trajectory of the object 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. © 2006 Elsevier B.V. All rights reserved.




Chernodub, M. N. (2006). A gauge-invariant object in non-Abelian gauge theory. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 634(2–3), 255–261. https://doi.org/10.1016/j.physletb.2006.01.062

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