Exact computation of loop averages in two-dimensional Yang-Mills theory

We present an explicit algorithm that allows the exact computation of all nonlocal gauge-invariant correlation functions in two-dimensional Yang-Mills theory. Explicit expressions are given for the expectation value of entangled loop operators and their products in the $\mathrm{U}\mathrm{}\left(N\right)\mathrm{}$ theory with arbitrary $N$.Using these results we show that the Schwinger-Dyson equation for loops holds without singularities in the continuum, and we verify the factorizability of the correlation functions in the $N\to \infty$ limit. A non-Abelian version of Stokes's theorem which is used in the calculations is derived for an arbitrary number of dimensions.