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

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

2000-08-03

arxiv.org/abs/hep-th/0008035v1

J.Exp.Theor.Phys. 92 (2001) 905-920

Physics

High Energy Physics

High Energy Physics - Theory

25 pages

Scientific paper

10.1134/1.1385630

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.

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