Intersections of Twisted Forms: New Theories and Double Copies

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.