Scattering Amplitudes, Tilings of Moduli Spaces and Positive Geometry

We will explore the relationship between the moduli space M0n of n points on the projective line and scattering amplitudes for the simplest Quantum Field Theory, the cubic biadjoint scalar. We discuss a natural set of “u-variable” coordinates on M0n which satisfy a miraculous set of binary-type identities, and which are used to define a certain canonical form which has singularities on the boundary strata of a “curvy” associahedron in M0n. We ask the same questions for 6 points in the projective plane and produce a similarly beautiful curvy polytope and set of binary-type identities, and a differential form which has singularities on the boundary strata, connecting to the moduli space of del Pezzo surfaces. Time permitting, we may discuss some appearances of oriented matroids in physics. References: 1912.11764, 2306.13604 and 2212.11243.

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Date published: Wednesday, September 27, 2023