  Schwarz-Christoffel (SC) mapping plays a crucial role in the calculation of
the large-size expansion for polygonal Wilson loops in confining gauge theories
using effective string theory (EST). Recently a new analytical regularization
based on SC mapping was suggested and successfully applied to the calculation
of the two-loop contribution of EST in the case of triangular Wilson loops. We
prove that this analytical renormalization produces finite results for
arbitrary polygonal Wilson loops and show that the result of the analytical
renormalization for a given polygonal contour is independent of the choice of
SC mapping for this polygon.
