Heterotic twistor–string theory

We reformulate twistor–string theory as a heterotic string based on a twisted (0,2)(0,2) model. The path integral localizes on holomorphic maps, while the (0,2)(0,2) moduli naturally correspond to the states of N=4N=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=4N=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.