Properties of Yang-Mills scattering forms

TL;DR

This paper explores the properties of scattering forms on moduli spaces of Riemann spheres, highlighting their invariance, boundary singularities, and factorization properties related to scattering amplitudes.

Contribution

It introduces the mathematical structure of scattering forms on moduli spaces, connecting their properties to physical scattering amplitudes and their boundary behaviors.

Findings

Singularities occur only at the boundary of the moduli space.

All singularities are logarithmic.

Residues factorize into lower-point differential forms.

Abstract

In this talk we introduce the properties of scattering forms on the compactified moduli space of Riemann spheres with $n$ marked points. These differential forms are $\text{PSL}(2,\mathbb{C})$ invariant, their intersection numbers correspond to scattering amplitudes as recently proposed by Mizera. All singularities are at the boundary of the moduli space and each singularity is logarithmic. In addition, each residue factorizes into two differential forms of lower points.