On Wilson loops for two touching circles with opposite orientation

We study the Wilson loops for contours formed by a consecutive passage of two touching circles with
a common tangent, but opposite orientation. The calculations are performed in lowest nontrivial
order for ##IMG## [http://ej.iop.org/images/1751-8121/52/9/095401/aab0003ieqn001.gif] SYM at weak
and strong coupling and for QCD at weak coupling. After subtracting the standard linear divergence
proportional to the length, as well the recently analysed spike divergence, we get for the
renormalised Wilson loops ##IMG##
[http://ej.iop.org/images/1751-8121/52/9/095401/aab0003ieqn002.gif] . The result holds for circles
with different radii and arbitrary angle between the discs spanned by them.

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