beyond the planar limit

Much of the most advanced work on the N=4 theory takes place in the “planar limit” or “planar approximation”. In this limit, one only considers Feynman diagrams that are planar. This limit goes back 40 years to ‘t Hooft’s large-N expansion of gauge theories, which has also played a large part in AdS/CFT.

Now we are beginning to see hopes for progress beyond the planar limit, here, here, and here.

For context, perhaps consider the first picture from Beisert et al.