Supersymmetric Born-Infeld from the Pure Spinor Formalism of the Open   Superstring
  Classical BRST invariance in the pure spinor formalism for the open superstring is shown to imply the supersymmetric Born-Infeld equations of motion for the background fields. These equations are obtained by requiring that the left and right-moving BRST currents are equal on the worldsheet boundary in the presence of the background. The Born-Infeld equations are expressed in N=1 D=10 superspace and include all abelian contributions to the low-energy equations of motion, as well as the leading non-abelian contributions. 
Nathan Berkovits and Vladimir Pershin (IFT/UNESP, Sao Paulo)