Exceptional conformal anomaly of null polygonal Wilson loops

We analyse the breaking of conformal invariance for null polygonal Wilson loops in ${\cal N}=4$ SYM beyond that induced by the UV divergences due to the cusps. It only shows up in exceptional configurations, where the polygon intersects the critical light cone of an inversion or a special conformal transformation. In comparison with the related study for the Euclidean version by Drukker and Gross, we find different leading terms both for weak as well as for strong coupling. Hence the conformal anomaly due to intersections of a null polygon with a critical light cone defines a new universal function of the coupling constant.