Scattering Amplitudes from Intersection Theory
Sebastian Mizera
TL;DR
This paper introduces a new mathematical formula for calculating intersection numbers of twisted cocycles using Picard-Lefschetz theory, linking them to scattering amplitudes in quantum field theory.
Contribution
It provides a novel proof connecting intersection theory with scattering amplitudes via a new formula derived from hyperplane arrangements.
Findings
New formula for intersection numbers using Picard-Lefschetz theory
Connection between intersection numbers and scattering amplitudes in CHY formulation
Mathematical framework applicable to moduli spaces of punctured Riemann spheres
Abstract
We use Picard-Lefschetz theory to prove a new formula for intersection numbers of twisted cocycles associated to a given arrangement of hyperplanes. In a special case when this arrangement produces the moduli space of punctured Riemann spheres, intersection numbers become tree-level scattering amplitudes of quantum field theories in the Cachazo-He-Yuan formulation.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.