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

We solve the superspace Bianchi identities for ten-dimensional supersymmetr ic Yang-Mills theory without imposing any kind of constraints apart from th e standard conventional one. In this way we obtain a set of algebraic condi tions on certain fields which in the on-shell theory are constructed as com posite ones out of the physical fields. These conditions must hence be sati sfied by any kind of theory in ten dimensions invariant under supersymmetry and some, abelian or non-abelian, gauge symmetry. Deformations of the ordi nary SYM theory (as well as the fields) are identified as elements of a cer tain spinorial cohomology, giving control over field redefinitions and the distinction between physically relevant higher-order corrections and those removable by field redefinitions. The conditions derived severely constrain theories involving F-2-level terms plus higher-order corrections, as for i nstance those derived from open strings as effective gauge theories on D-br anes.