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

Abstract

We show that the Wilson loop operator for 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, we 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.

48 pages, 8 figures; minor changes, version to be published in Physical Review D

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Cited by in corpus (28)

• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• Toward a first-principle derivation of confinement and chiral-symmetry-breaking crossover transitions in QCD
• Reformulating SU(N) Yang-Mills theory based on change of variables
• A low-energy effective Yang-Mills theory for quark and gluon confinement
• Perfect Abelian dominance of quark confinement in SU(3) QCD
• New descriptions of lattice SU(N) Yang-Mills theory towards quark confinement
• Non-Abelian Dual Superconductor Picture for Quark Confinement
• The static quark potential from the gauge invariant Abelian decomposition
• Gauge-invariant description of Higgs phenomenon and quark confinement
• The exact decomposition of gauge variables in lattice Yang-Mills theory
• Magnetic monopoles and center vortices as gauge-invariant topological defects simultaneously responsible for confinement
• Gauge-independent "Abelian" and magnetic-monopole dominance, and the dual Meissner effect in lattice $SU(2)$ Yang-Mills theory
• Non-Abelian dual superconductivity in SU(3) Yang-Mills theory: dual Meissner effect and type of the vacuum
• Proving Abelian dominance in the Wilson loop operator
• QCD Flux Tubes and Anomaly Inflow
• The Static Quark Potential from the Gauge Independent Abelian Decomposition
• Berry phase in the phase space worldline representation: the axial anomaly and classical kinetic theory
• Non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation and its implication to quark confinement
• Magnetic Monopole Loops supported by a Meron pair as the Quark Confiner
• Jackiw-Nohl-Rebbi two-instanton as a source of magnetic monopole loop
• Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field
• Gauge gravity vacuum in constraintless Clairaut-type formalism
• String tension from gauge invariant Magnetic Monopoles
• Angular Momentum Inheritance from the Schwinger Effect in (Chromo)electromagnetic Fields
• How to extract the dominant part of the Wilson loop average in higher representations
• Complete Monopole Dominance of the Yang-Mills Confining Potential
• Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice
• Reformulations of the Yang-Mills theory toward quark confinement and mass gap