Propagators for Generalized Scattering Amplitudes via tropical combinatorics

by Dr Nick Early (MPP)

Friday 4 Mar 2022, 11:00 → 12:00 Europe/Berlin

Main/0-174 - Auditorium + Zoom (Main)

The Cachazo-He-Yuan (CHY) scattering equations formalism provides a kind of Swiss army knife for scattering amplitudes: by swapping in different combinations from a set of possible integrands one obtains expressions for scattering amplitudes for an expanse of Quantum Field Theories, including the cubic scalar, Dirac-Born-Infeld, NLSM, and Yang-Mills and variants.  At the heart of the construction is a Morse function on the modulo space $\mathcal{M}_{0,n}$ of $n$ points on the projective line.

In this talk, I present a first principle construction of a framework, which uses combinatorial and tropical geometry to calculate tree amplitudes.  Possible generalizations of this framework hint to the existence of an undiscovered class of higher dimensional theories, as evidenced by recent joint work with Cachazo, Guevara, Mizera (CEGM), in which the CHY formula for the cubic scalar was extended to projective spaces $\mathbb{CP}^{k-1}$.