Non-Abelian Stokes theorems in the Yang-Mills and gravity theories

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. (C) 2001 MAIK Nauka/ Interperiodica.