Einstein Yang-Mills amplitudes from intersections of twisted forms

Abstract

We present a geometric derivation of all-multiplicity (single-trace) tree-level Einstein Yang-Mills (EYM) amplitudes $$ \mathcal{A} $$ 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 α′ → ∞ 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 α′ → ∞ limit. Finally, we present an all-multiplicity decomposition formula of any EYM amplitude $$ \mathcal{A} $$ A (n; r) as linear combination over (m − 3)! pure m gluon subamplitudes.

One-loop amplitudes in Einstein-Yang-Mills from forward limits

“…The double-copy structure of EYM implies relations between EYM amplitudes and those of (super-)Yang-Mills. At tree level, such EYM amplitude relations have been analyzed from a multitude of perspectives including open strings interacting with closed strings [16,17], the Cachazo-He-Yuan (CHY) formalism 2 [24][25][26][27][28], heterotic strings [29], gauge invariance [30,31] and the color-kinematics duality of YM+φ 3 [32]. Similar doublecopy structures and resulting tree-amplitude relations apply to conformal supergravity coupled to gauge theories [12,33].…”