Algebraic Combinatorics Seminar - Hugh Thomas

Title: Scattering amplitudes and associahedra

Abstract:

The classic approach to scattering amplitudes sums a contribution from a (potentially very large) number of Feynman diagrams. Over the past decade, Arkani-Hamed and his collaborators have developed a new approach, in which the sum of Feynman diagrams is replaced by a single geometrical object. For N=4 SYM, this object is now known as the​​​​​​​ amplituhedron. More recently, Arkani-Hamed, Bai, He, and Yan, studying a simpler (biadjoint scalar phi-cubed) quantum field theory, discovered that the object playing the role of the amplituhedron is in fact a well-known polytope: the associahedron, originally defined by Stasheff some fifty years ago in the context of algebraic topology, with a lovely combinatorial structure which I shall explain. I will present​​​​​​​ Arkani-Hamed's approach using this simple model as an example, and discuss some subsequent work in collaboration with Arkani-Hamed, He, and​​​​​​​ Salvatori, in which we were led to define an infinite-dimensional​​​​​​​ associahedron. I will not assume previous familiarity with either scattering amplitudes or associahedra.