Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms

TL;DR

This paper introduces a geometric approach to derive all-multiplicity Einstein Yang-Mills amplitudes using twisted forms on moduli space, connecting string theory and CHY formulas through intersection theory.

Contribution

It provides a novel geometric derivation of EYM amplitudes via twisted intersection numbers, linking superstring amplitudes to CHY formulas in the infinite tension limit.

Findings

Derived EYM amplitudes from twisted intersection numbers on moduli space.

Connected superstring disk amplitudes to CHY formulas through a geometric map.

Presented a decomposition of EYM amplitudes into pure gluon subamplitudes.

Abstract

We present a geometric derivation of all-multiplicity (single-trace) tree-level Einstein Yang-Mills (EYM) amplitudes ${\cal A}(n;r)$ involving $n$ gluons and $r$ gravitons by a bilinear of two twisted differential forms on the moduli space of Riemann spheres with $m\!:=\!n\!+\!r$ punctures. The differential forms are gained by studying the underlying superstring disk amplitude and proposing an embedding of the disk onto the sphere. This map can be interpreted as a geometrical map from the open superstring to a heterotic or ambitwistor string structure. Then, the twisted intersection number of the two $m$-forms, which is obtained by integrating over the moduli space of Riemann sphere with $m$ punctures, reproduces in the infinite inverse string tension limit $\alpha'\!\rightarrow\! \infty$ the corresponding CHY formula of the EYM amplitude. To bolster our findings we study the disk amplitude of open and closed strings using the Grassmann description of the underlying superstring amplitude, map it to a closed string amplitude and consider the $\alpha'\!\rightarrow\! \infty$ limit. Finally, we present an all-multiplicity decomposition formula of any EYM amplitude ${\cal A}(n;r)$ as linear combination over $(m\!-\!3)!$ pure $m$ gluon subamplitudes.