Non-commutative superspace from string theory

Turning on background fields in string theory sometimes has an alternative interpretation as a deformation of the target space geometry. A particularly well-known case is the NS–NS two form B, which gives rise to spacetime non-commutativity. In this Letter we point out that this phenomenon extends to ten-dimensional superspace when employing a covariant quantization of the superstring, generalizing an observation by Ooguri and Vafa in four dimensions. In particular, we will find that RR field strengths give rise to a non-zero {θ,θ} anti-commutator, just as in four dimensions, whereas the gravitino yields a non-zero value for [x,θ].