ZhETF, Vol. 119,
No. 6,
p. 1050 (June 2001)
(English translation - JETP,
Vol. 92, No. 6,
p. 905,
June 2001
available online at www.springer.com
)
NON-ABELIAN STOKES THEOREMS IN YANG-MILLS AND GRAVITY THEORIES
Diakonov D., Petrov V.
Received: February 1, 2001
PACS: 11.15.Ha, 12.38.Gc
We discuss the interpretation of the non-Abelian Stokes theorem for 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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