Scattering amplitudes are where quantum field theory directly meets collider experiments. An excellent model for scattering in QCD is provided by N=4 super-Yang-Mills theory, particularly in the planar limit of a large number of colors, where the theory becomes integrable. The first nontrivial amplitude in this theory is for 6 gluons. It can be computed to 7 loops using a bootstrap based on the rigidity of the function space of multiple polylogarithms, together with a few other conditions. One can also bootstrap a particular form factor, for the chiral stress-tensor operator to produce 3 gluons, through 8 loops. This form factor is the N=4 analog of the LHC process, gluon gluon --> Higgs + gluon. Remarkably, the two sets of results are related by a mysterious `antipodal' duality, which exchanges the role of branch cuts and derivatives. Furthermore, this duality is `explained' by an antipodal self-duality of the 4 gluon form factor of the same operator; although it is still fair to say of the self-duality, `who ordered that?'
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