Supersymmetric corrections to eleven-dimensional supergravity

In this paper we study eleven-dimensional supergravity in its most generalform. This is done by implementing manifest supersymmetry (and Lorentzinvariance) through the use of the geometric (torsion and curvature) superspaceBianchi identities. These identities are solved to linear order in adeformation parameter introduced via the dimension zero supertorsion given inits most general form. The theory so obtained is referred to as the deformedtheory (to avoid the previously used term "off-shell"). An important by-productof this result is that any higher derivative correction to ordinarysupergravity of the same dimension as R^4, but not necessarily containing it,derived e.g. from M-theory, must appear in a form compatible with the equationsobtained here. Unfortunately we have not yet much to say about the explicitstructure of these corrections in terms of the fields in the masslesssupermultiplet. Our results are potentially powerful since if the dimensionzero torsion could be derived by other means, our reformulation of the Bianchiidentities as a number of algebraic relations implies that the full theorywould be known to first order in the deformation, including the dynamics. Wemention briefly some methods to derive the information needed to obtainexplicit answers both in the context of supergravity and ten-dimensionalsuper-Yang-Mills where the situation is better understood. Other relevantaspects like spinorial cohomology, the role of the 3- and 6-form potentials andthe connection of these results to M2 and M5 branes are also commented upon.Comment: 62 pp., JHEP styl