Marginal Deformations of Tree-Level N=4 SYM from Twistor String Theory

The topological B-model with target the supertwistor space CP(3|4) is known to describe perturbative amplitudes of N=4 Super Yang-Mills theory. We review the extension of this correspondence to the superconformal gauge theories that arise as marginal deformations of N=4 by considering the effects of turning on a certain closed string background, which results in non-anticommutativity in the fermionic directions of CP(3|4). We generalise the twistor string prescription for amplitudes to this case and illustrate it with some simple examples.