  We consider polygonal Wilson loops with null edges in conformal gauge
theories. We derive an OPE-like expansion when several successive lines of the
polygon are becoming aligned. The limit corresponds to a collinear, or
multicollinear, limit and we explain the systematics of all the subleading
corrections, going beyond the leading terms that were previously considered.
These subleading corrections are governed by excitations of high spin
operators, or excitations of a flux tube that goes between two Wilson lines.
The discussion is valid for any conformal gauge theory, for any coupling and in
any dimension. For N=4 super Yang Mills we check this expansion at strong
coupling and at two loops at weak coupling . We also make predictions for the
remainder function at higher loops. In the process, we also derived a new
version for the TBA integral equations that determine the strong coupling
answer and present the area as the associated Yang-Yang functional.
