Theoretical Physics Wednesday Seminar: Song He

Generalized Particles and Strings from Combinatorial Geometries

The search for a "theory at infinity” for the S-Matrix has revealed surprising geometric structures underlying scattering amplitudes. I will present a novel picture where certain scattering amplitudes of both particles and strings directly emerge from polytopes known as generalized associahedra. I will show how tree- and one-loop amplitudes for bi-adjoint scalars are given by “volume forms” of such associahedra living in kinematic space, and how (generalized) associahedra for string worldsheet and (generalized) string integrals defined on them naturally arise in this construction. The field-theory limit of such string-like integral is given by the pushforward using scattering equations that map worldsheet associahedra to kinematic ones, and I will show that in fact this last result applies to any polytopes.