Talk

Aspects of Grassmannian scattering amplitudes

  • Bruno Gimenez Umbert (University of Southampton)
G3 10 (Lecture hall)

Abstract

This talk will consist of two parts. In the first part I will review how to compute n-point scattering amplitudes in the ϕ3 theory from three different approaches. The first approach is using Feynman diagrams, which is the standard way to compute these observables in physics. Then I will explain how the tropical Grassmannian, TropG(2,n), is closely related to the space of the Feynman diagrams for this theory, and I will propose a formula as an integral over TropG(2,n) to compute first ϕ3 and then ϕp scattering amplitudes, for any p>2. The third approach is the CHY formula, which is an integral over the moduli space of n points on CP1. In the second part of the talk, motivated by the isomorphism between the Grassmannians G(2,n) and G(n-2,n), I will explain how to generalize the CHY formula to an integral over the space of n points on higher dimensional projective spaces CPk1, thus providing a natural generalization of the notion of scattering amplitudes. I will also point out connections with higher dimensional tropical Grassmannians and will comment on some of the features of these new objects.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

Anna-Laura Sattelberger

MPI for Mathematics in the Sciences Contact via Mail