Certain scattering amplitudes in N=4 D=4 super Yang-Mills theory and neighbouring gauge theories – called maximally helicity violating amplitudes (“MHV amplitudes”) simplify drastically as compared to the generic situation and in fact are controled by a certain twistor string theory whose target space is a twistor space. See (Monteiro) for a review.
A light-cone QCD–Lagrangian density adapted to MHV -amplitudes:
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