Derivative corrections in 10-dimensional super-Maxwell theory
  We construct the supersymmetric effective action at order alpha'^4 of the abelian open superstring. It includes the alpha'^4 terms in the abelian Born-Infeld action, and in particular the leading derivative correction of the form d^4F^4. Besides linear supersymmetry this sector of the open string effective action also has a nonlinear supersymmetry. The terms d^4F^4 and their fermionic partners have an arbitrary coefficient, and we discuss the possible fate of such coefficients when higher orders in alpha' are included. 
Andres Collinucci, Mees de Roo and Martijn G.C. Eenink