Spinorial cohomology of abelian d=10 super-Yang-Mills at alpha'^3
  We compute the spinorial cohomology of ten-dimensional abelian SYM at order alpha'^3 and we find that it is trivial. Consequently, linear supersymmetry alone excludes the presence of alpha'^3-order corrections. Our result lends support to the conjecture that there may be a unique supersymmetric deformation of ordinary ten-dimensional abelian SYM. 
Martin Cederwall, Bengt E.W. Nilsson and Dimitrios Tsimpis