Ambitwistor strings in 4-dimensions

TL;DR

The paper develops four-dimensional ambitwistor string theories using twistors and dual twistors to produce compact, tree-level formulae for gauge and gravitational amplitudes with arbitrary supersymmetry. By constraining ambitwistor space with $Z\cdot W=0$ and formulating worldsheet spinor fields, it derives integrated vertex operators and correlators that localize on refined scattering equations tied to the N^kMHV degree. Yang-Mills amplitudes arise from correlators of twistor/dual-twistor vertex operators with Parke-Taylor structures, while gravity amplitudes are captured by a determinant of a contracted matrix $\mathcal{H}$, yielding results consistent with known Cachazo–He–Song/Cachazo–Skinner representations. The framework unifies and simplifies prior twistor-string approaches and points to loop extensions and AdS/dS applications, subject to anomaly considerations and potential critical-matter completions.

Abstract

We develop ambitwistor string theories for 4 dimensions to obtain new formulae for tree-level gauge and gravity amplitudes with arbitrary amounts of supersymmetry. Ambitwistor space is the space of complex null geodesics in complexified Minkowski space, and in contrast to earlier ambitwistor strings, we use twistors rather than vectors to represent this space. Although superficially similar to the original twistor string theories of Witten, Berkovits and Skinner, these theories differ in the assignment of worldsheet spins of the fields, rely on both twistor and dual twistor representatives for the vertex operators, and use the ambitwistor procedure for calculating correlation functions. Our models are much more flexible, no longer requiring maximal supersymmetry, and the resulting formulae for amplitudes are simpler, having substantially reduced moduli. These are supported on the solutions to the scattering equations refined according to MHV degree and can be checked by comparison with corresponding formulae of Witten and of Cachazo and Skinner.