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Twistor space constructions and actions are given for full Yang-Mills andconformal gravity using almost complex structures that are not, in general,integrable. These are used as the basis of a derivation of the twistor-stringgenerating functionals for tree level perturbative scattering amplitudes ofYang-Mills and conformal gravity. The derivation follows by expanding andresumming the classical approximation to the path integral obtained from thetwistor action. It provides a basis for exploring whether the equivalence canbe made to extend beyond tree level and allows one to disentangle conformalsupergravity modes from the Yang-Mills modes.Comment: 23 pages. v2: typos etc. corrected, some extra clarifying remarks,  particularly in section

Twistor actions for non-self-dual fields; a new foundation for twistor-string theory