  We consider a light-like Wilson loop in N=4 SYM evaluated on a regular
n-polygon contour. Sending the number of edges to infinity the polygon
approximates a circle and the expectation value of the light-like WL is
expected to tend to the localization result for the circular one. We show this
explicitly at one loop, providing a prescription to deal with the divergences
of the light-like WL and the large n limit. Taking this limit entails
evaluating certain sums of dilogarithms which, for a regular polygon, evaluate
to the same constant independently of n. We show that this occurs thanks to
underpinning dilogarithm identities, related to the so-called polylogarithm
ladders, which appear in rather different contexts of physics and mathematics
and enable us to perform the large n limit analytically.
