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

TL;DR

This paper develops twistor space actions for full Yang-Mills and conformal gravity using non-integrable almost complex structures, deriving twistor-string generating functionals for tree-level scattering amplitudes and exploring potential extensions beyond tree level.

Contribution

It introduces a novel twistor space formulation for non-self-dual fields and derives tree-level twistor-string generating functionals for Yang-Mills and conformal gravity.

Findings

Derived twistor-string generating functionals for tree-level amplitudes.

Provided a framework to explore extensions beyond tree level.

Separated conformal supergravity modes from Yang-Mills modes.

Abstract

Twistor space constructions and actions are given for full Yang-Mills and conformal gravity using almost complex structures that are not, in general, integrable. These are used as the basis of a derivation of the twistor-string generating functionals for tree level perturbative scattering amplitudes of Yang-Mills and conformal gravity. The derivation follows by expanding and resumming the classical approximation to the path integral obtained from the twistor action. It provides a basis for exploring whether the equivalence can be made to extend beyond tree level and allows one to disentangle conformal supergravity modes from the Yang-Mills modes.