Title: The SU (N) Wilson loop average in two dimensions
Abstract: We solve explicitly a closed, linear loop equation for the SU(2) Wilson loop average on a two-dimensional plane and generalize the solution to the case of the SU(N) Wilson loop average with an arbitrary closed contour. Furthermore, the flat space solution is generalized to any two-dimensional manifold for the SU(2) Wilson loop average and to any two-dimensional manifold of genus O for the SU(N) Wilson loop average. The SU(N) Wilson loop average folows an area law W(C) = ΣrP'r exp[ - Σijri2Si], where jri2 is the quadratic Casimir operator for the window with area Si. Only certain combinations of the Casimir operators are allowed in the sum over i. We give a physical interpretation of the constants Pr1 in the case of a non self-intersecting composed path C and of the constraints determining in which combinations the Casimir operators occur.