Einstein Supergravity and New Twistor String Theories

TL;DR

The paper constructs anomaly-free twistor-string theories by gauging currents tied to the infinity twistor, enabling target-space theories with Einstein (second-order) gravity coupled to Yang–Mills while breaking conformal invariance. It identifies two main anomaly-free classes: one in $N=4$ super-twistor space yielding $N=4$ Einstein supergravity plus $N=4$ super-Yang–Mills, and another yielding $N=8$ Einstein supergravity, with a spectrum organized by ghost-free vertex operators. A concrete computation of a nontrivial three-graviton amplitude for the $N=8$ and $N=4$ theories shows consistency with Einstein gravity cubic couplings, supporting nontrivial interactions. The work highlights a decoupling limit where gravity can vanish to recover pure YM amplitudes, and discusses how these models differ from prior twistor strings by explicitly breaking conformal invariance, thereby potentially enabling realistic gravity-Yang–Mills dynamics within a twistor framework.

Abstract

A family of new twistor string theories is constructed and shown to be free from world-sheet anomalies. The spectra in space-time are calculated and shown to give Einstein supergravities with second order field equations instead of the higher derivative conformal supergravities that arose from earlier twistor strings. The theories include one with the spectrum of N=8 supergravity, another with the spectrum of N=4 supergravity coupled to N=4 super-Yang-Mills, and a family with $N\ge 0$ supersymmetries with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills. The non-supersymmetric string with N=0 gives self-dual gravity coupled to self-dual Yang-Mills and a scalar. A three-graviton amplitude is calculated for the N=8 and N=4 theories and shown to give a result consistent with the cubic interaction of Einstein supergravity.