Abstract
We discuss the interpretation of the non-Abelian Stokes theorem or the Wilson loop in the Yang-Mills theory. For the “gravitational Wilson loops,” i.e., holonomies in curved d=2, 3, 4 spaces, we then derive “ non-Abelian Stokes theorems” that 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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From Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 119, No. 6, 2001, pp. 1050–1066.
Original English Text Copyright © 2001 by Diakonov, Petrov.
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Diakonov, D.I., Petrov, V.Y. Non-Abelian Stokes theorems in the Yang-Mills and gravity theories. J. Exp. Theor. Phys. 92, 905–920 (2001). https://doi.org/10.1134/1.1385630
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DOI: https://doi.org/10.1134/1.1385630