Loops in Twistor Space

We elucidate the one-loop twistor-space structure corresponding to momentum-space MHV diagrams. We also discuss the infrared divergences, and argue that only a limited set of MHV diagrams contain them. We show how to introduce a twistor-space regulator corresponding to dimensional regularization for the infrared-divergent diagrams. We also evaluate explicitly the `holomorphic anomaly' pointed out by Cachazo, Svrcek, and Witten, and use the result to define modified differential operators which can be used to probe the twistor-space structure of one-loop amplitudes.