Geometric Recursion from Polytope Triangulations and Twisted Homology

TL;DR

This paper introduces a geometric method for deriving recursion relations in scattering amplitudes using polytope triangulations and twisted homology, linking topological conditions to divergence cancellations.

Contribution

It presents a novel geometric framework connecting polytope triangulations and topological homology to recursion relations in scattering amplitudes.

Findings

Intersection numbers of triangulated accordiohedra are computed.

Spurious divergences are canceled via a topological no-boundary condition.

The approach provides a new geometric perspective on amplitude recursion relations.

Abstract

A geometric approach to understanding recursion relations for scattering amplitudes is developed. We achieve this by studying intersection numbers of triangulated accordiohedra presented as hyperplane arrangements. The cancellation of spurious divergences is subsequently realized as a topological no-boundary condition.