Non-Abelian Stokes Theorems in Yang-Mills and Gravity Theories

Abstract

We recall the non-Abelian Stokes theorem for the Wilson loop in the Yang-Mills theory and discuss its meaning. Then we move to `gravitational Wilson loops', i.e. to holonomies in curved d=2,3,4 spaces and derive non-Abelian Stokes theorems for these quantities as well, which are similar to our formula in the Yang-Mills theory. In particular we derive an elegant formula for the holonomy in the case of a constant-curvature background in three dimensions and a formula for small-area loops in any number of dimensions.

25 pages

References in corpus (3)

• Dual gluons and monopoles in 2+1 dimensional Yang-Mills theory
• Yang-Mills Theory in Three Dimensions as Quantum Gravity Theory
• Gauge-invariant formulation of the d=3 Yang-Mills theory

Cited by in corpus (11)

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• In pursuit of Pomeron loops: the JIMWLK equation and the Wess-Zumino term
• More Remarks on High Energy Evolution
• Wilson loop and magnetic monopole through a non-Abelian Stokes theorem
• Mapping the braiding properties of the Moore-Read state
• Different faces of confinement
• Wilson loops in CDT quantum gravity
• Magnetic Monopole Loops supported by a Meron pair as the Quark Confiner
• Large Dual Transformations and the Petrov-Diakonov Representation of the Wilson Loop
• On the non-Abelian Stokes theorem for SU(2) gauge fields
• Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field