  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.
