N-Point Tree-Level Scattering Amplitude in the New Berkovits' String

TL;DR

This work provides a direct tree-level proof that Berkovits' twistor-like pure spinor string reproduces ten-dimensional ${\mathcal N}=1$ SYM in the heterotic version and ten-dimensional type II SUGRA in the respective version, aligning with CHY-type scattering for gluons and gravitons. The analysis shows that X-space and phase-space integrations yield the scattering equations and momentum conservation, and that the amplitudes factorize through CHY and KLT structures, with SUGRA emerging as a double copy of YM. The results establish a concrete bridge between the Berkovits construction and CHY/scattering-equation formalisms, clarifying how supersymmetry is encoded and how known SYM/SUGRA amplitudes arise in this twistor-like string framework. The discussion highlights potential loop extensions, the infinite-tension limit, and the search for a manifest SUSY integrand within this setup, underscoring the framework's relevance for broader amplitude program developments.

Abstract

We give a proof by direct computation that at tree level, the twistor-like superstring theory in the pure spinor formalism proposed very recently by Berkovits describes ten-dimensional N=1 super Yang-Mills in its heterotic version, and type II supergravity in its type II version. The Yang-Mills case agrees with the result obtained by Mafra, Schlotterer, Stieberger and Tsimpis. When restricting to gluon and graviton scattering, this new theory gives rise to Cachazo-He-Yuan formula.