We start with an n-point correlation function in a conformal gauge theory. We
show that a special limit produces a polygonal Wilson loop with n sides. The
limit takes the n points towards the vertices of a null polygonal Wilson loop
such that successive distances xi,i+12→0. This produces a fast moving
particle that generates a "frame" for the Wilson loop. We explain in detail how
the limit is approached, including some subtle effects from the propagation of
a fast moving particle in the full interacting theory. We perform perturbative
checks by doing explicit computations in N=4 super-Yang-Mills.Comment: 37 pages, 10 figures; typos corrected, references adde