D = 10 super-Yang-Mills at O(α′2)

Using superspace techniques, the complete and most general action of D=10super-Yang--Mills theory is constructed at the alpha'^2 level. No otherapproximations, e.g., keeping only a subset of the allowed derivative terms,are used. The Lorentz structure of the alpha'^2 corrections is completelydetermined, while (depending on the gauge group) there is some freedom in theadjoint structure, which is given by a totally symmetric four-index tensor. Weexamine the second, non-linearly realised supersymmetry that may be presentwhen the gauge group has a U(1) factor, and find that the constraints fromlinear and non-linear supersymmetry to a large extent coincide. However, theadditional restrictions on the adjoint structure of the order alpha'^2interactions following from the requirement of non-linear supersymmetry do notcompletely specify the symmetrised trace prescription.Comment: 19 pp., plain te