Supersymmetric gauge theories in twistor space

We construct a twistor space action for N = 4 super Yang-Mills theory and show that it is equivalent to its four dimensional spacetime counterpart at the level of perturbation theory. We compare our partition function to the original twistor-string proposal, showing that although our theory is closely related to string theory, it is free from conformal supergravity. We also provide twistor actions for gauge theories with N < 4 supersymmetry, and show how matter multiplets may be coupled to the gauge sector.