Spinorial cohomology and maximally supersymmetric theories

Fields in supersymmetric gauge theories may be seen as elements in aspinorial cohomology. We elaborate on this subject, specialising to maximallysupersymmetric theories, where the superspace Bianchi identities, aftersuitable conventional constraints are imposed, put the theories on shell. Inthese cases, the spinorial cohomologies describe in a unified manner gaugetransformations, fields and possible deformations of the models, e.g.string-related corrections in an alpha' expansion. Explicit cohomologies arecalculated for super-Yang-Mills theory in D=10, for the N=(2,0) tensormultiplet in D=6 and for supergravity in D=11, in the latter case from thepoint of view of both the super-vielbein and the super-3-form potential. Thetechniques may shed light on some questions concerning the alpha'-correctedeffective theories, and result in better understanding of the role of the3-form in D=11 supergravity.Comment: 23 pp, plain tex. v2: Minor changes, references adde