Heterotic twistor-string theory

TL;DR

This work reframes twistor-string theory as a heterotic, twisted (0,2) theory whose path integral localizes on holomorphic maps to twistor space, with Penrose-transform states corresponding to linearized N=4 conformal supergravity and super Yang-Mills. By promoting the (0,2) model to a full string theory, it derives vertex operators for moduli deformations, couples to YM via a worldsheet current algebra, and obtains a twistor-space action that matches known twistor-string amplitudes and actions. The formulation clarifies relations among Witten’s B-model, Berkovits’ model, and D-brane constructions, while offering a contour-integral interpretation of amplitudes and a route to nonperturbative inclusions via NS branes and instantons. It also connects the googly data and selfdual sectors to deformations of the complex structure and B-field on supertwistor space, with links to generalized geometry and a broader, signature-flexible framework. The overall framework provides a unified, anomaly-consistent path to reproduce N=4 SYM plus conformal supergravity amplitudes and actions from twistor space, while suggesting new avenues for extending to other spacetime theories and signatures.

Abstract

We reformulate twistor-string theory as a heterotic string based on a twisted (0,2) model. The path integral localizes on holomorphic maps, while the (0,2) moduli naturally correspond to the states of N=4 super Yang-Mills and conformal supergravity under the Penrose transform. We show how the standard twistor-string formulae of scattering amplitudes as integrals over the space of curves in supertwistor space may be obtained from our model. The corresponding string field theory gives rise to a twistor action for N=4 conformal supergravity coupled to super Yang-Mills. The model helps to explain how the twistor-strings of Witten and Berkovits are related and clarifies various aspects of each of these models.