Lance Dixon (SLAC)
Polylogarithmic Polygon Origami
Scattering amplitudes in planar N=4 super-Yang-Mills theory are dual to light-like polygonal Wilson-loop expectation values. In many cases their perturbative expansion can be expressed in terms of multiple polylogarithms which also obey certain single-valuedness conditions or branch cut restrictions. The rigidity of this function space, together with a few other conditions, allows one to construct the six-point amplitude -- or hexagonal Wilson loop -- through 6 loops, and the (symbol of the) seven-point amplitude through 4 loops. Then one can "fold" the polygonal Wilson loops into multiple degenerate configurations, expressing the limiting behavior in terms of simpler function spaces, and learning in the process about how amplitudes factorize. The polylogarithms, and the multiple zeta values to which they evaluate at specific points, satisfy a Hopf algebra coproduct structure, and additional relations coming from "Cosmic Galois Theory".