Novel Mathematical Structures in N = 4 Supersymmetric Yang-Mills Theory
OKC/Nordita High-Energy Physics Theory seminar
Monday 12 February 2018
to 14:15 at
Nordita East Building
Andrew McLeod (NBI)
While traditional methods for calculating scattering amplitudes prove too computationally intensive to be useful at higher loop orders, a great deal is now known about the analytic and kinematic properties of amplitudes to all orders in planar N=4. This information can be leveraged to construct these amplitudes directly, by putting together an ansatz of the relevant class of functions and requiring that it share the distinctive properties of a given amplitude. In this talk, I will describe how this bootstrap-type approach can be used to uniquely determine all six-particle amplitudes in this theory through (at least) six loops, focusing on how these methods make transparent the Steinmann relations. I will then describe two unexpected and striking mathematical structures that appear in these amplitudes---they respect a cosmic Galois `coaction principle' in the direction of increasing loop order, and their Poisson cobracket is `subalgebra-constructible' in the direction of increasing particle number (at least at low loop order). Finally, I will comment on how these methods and observations can assist calculations of quantities of direct relevance to particle physics experiments.