The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections

We solve the superspace Bianchi identities for ten-dimensional supersymmetricYang-Mills theory without imposing any kind of constraints apart from thestandard conventional one. In this way we obtain a set of algebraic conditionson certain fields which in the on-shell theory are constructed as compositeones out of the physical fields. These conditions must hence be satisfied byany kind of theory in ten dimensions invariant under supersymmetry and some,abelian or non-abelian, gauge symmetry. Deformations of the ordinary SYM theory(as well as the fields) are identified as elements of a certain spinorialcohomology, giving control over field redefinitions and the distinction betweenphysically relevant higher-order corrections and those removable by fieldredefinitions. The conditions derived severely constrain theories involvingF^2-level terms plus higher-order corrections, as for instance those derivedfrom open strings as effective gauge theories on D-branes.Comment: plain tex, 18 pp., 3 fig