Marginal deformations of tree‐level 𝒩 = 4 SYM from twistor string theory

The topological B–model with target the supertwistor space ℂP3|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 ℂP3|4. We generalise the twistor string prescription for amplitudes to this case and illustrate it with some simple examples.