Non-Abelian Stokes Theorems in Yang-Mills and Gravity Theories
High Energy Physics - Theory
2009-10-31 v1 General Relativity and Quantum Cosmology
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.
Keywords
Cite
@article{arxiv.hep-th/0008035,
title = {Non-Abelian Stokes Theorems in Yang-Mills and Gravity Theories},
author = {Dmitri Diakonov and Victor Petrov},
journal= {arXiv preprint arXiv:hep-th/0008035},
year = {2009}
}
Comments
25 pages