Intersections of Twisted Forms: New Theories and Double Copies

TL;DR

This paper develops a geometric framework using twisted differential forms on moduli spaces to compute scattering amplitudes and double-copy constructions for various theories, revealing new relationships and theories.

Contribution

It introduces a catalog of twisted differential forms and demonstrates how their intersection numbers can compute amplitudes and double-copy structures for both known and new theories.

Findings

Derived amplitude relations within intersection theory.

Constructed double-copy models for higher derivative gravity and bimetric gravity.

Identified new theories via intersection number pairings.

Abstract

Tree-level scattering amplitudes of particles have a geometrical description in terms of intersection numbers of pairs of twisted differential forms on the moduli space of Riemann spheres with punctures. We customize a catalog of twisted differential forms containing both already known and new differential forms. By pairing elements from this list intersection numbers of various theories can be furnished to compute their scattering amplitudes. Some of the latter are familiar through their CHY description, but others are unknown. Likewise, certain pairings give rise to various known and novel double-copy constructions of spin-two theories. This way we find double copy constructions for many theories, including higher derivative gravity, (partial massless) bimetric gravity and some more exotic theories. Furthermore, we present a derivation of amplitude relations in intersection theory.