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Résumé |
Amplitudes in planar N=4 super Yang-Mills theory exhibit fascinating analytic
properties which are intimately connected to cluster algebras. In this talk I will
describe a different language for uncovering these features based on the theory of
Gröbner bases for polynomial ideals. By applying this analysis to the Grassmannian
Plücker relations we will recover the singularities, or `symbol alphabet', and
cluster adjacency relations satisfied by the N=4 amplitudes. We will then
generalise this formalism to non-dual conformal and non-planar theories and show
how to recover the alphabet for massless five-point amplitudes in QCD and gravity. |
