SUPERGRAVITY P. van NIEUWENHUIZEN To Joel Scherk 0370 ...

380 P. van Nieuwenhuizen. SupergravilyMajorana spinor — Aspinor whose Majorana and Dirac conjugate are equal. In a Majorana representationfor the y matrices, it is a real spinor.Weyl spinors — Left- or right-handed spinors, i.e. eigenfunctions of (1 ± ys) with ~ = +1Majorana—Weyl spinors — Have both of the previous properties. This is possible only for space-times ofdimension D = 2 modulo 8.Rigid supersymmetry — Supersymmetry with constant parameters. The more familiar term globalsupersymmetry has the drawback that it is not meant to refer to global topological properties.Global supersymmetiy — See above.Local supersymmetry — Supersymmetry with spacetime dependent parameters.Simple supergravity models — Supersymmetric models in curved space-time, invariant under one SSTL.Extended supergravity models — Same as before, with “one” replaced by N (N 2).Supergravity — The domain of Mathematical Physics which studies simple (N = 1) or extended (N ~ 2)supergravity models.Gravitinos — The gauge particles of spin ~, associated with local, simple or extended supersymmetry.Gauge supermultiplet — The supermultiplet containing the graviton, the gravitinos and eventually (forN 2), lower spin fields.Pure supergravity — Simple or extended supergravity models based on a gauge supermultiplet with a selfcoupling K, of dimension the inverse of a mass, uncoupled to any matter multiplet.Super Higgs effect — The supersymmetric analog of the Higgs effect whereby, when supersymmetry isspontaneously broken, a gravitino (or several of them) “eats up” a goldstino (or several) andbecomes massive.Antigravity — A vectorial force, due to the exchange of a vector particle which is a member of anextended (N 2) gauge supermultiplet and which between two particles exactly cancels the gravitationalforce in the static limit, and doubles it between a particle and an antiparticle.Tetrad — The gauge fields of spin 2 which must be used instead of the metric when fermions arepresent.Vierbein — Same as tetrad.Supervielbein — Vierbein in superspace (viel = many in German).Graded Lie algebras — A Lie algebra with a grading. For example, the Lorentz group with k and j has aZ 2 grading.Superalgebras — A Z2 graded Lie algebra whose elements are “even” or “odd” such that the bracketrelation for two odd elements is symmetric, while also the super-Jacobi identity is satisfied. (Hence asuperalgebra is a graded algebra, but not the reverse.)Fierzing — Performing a Fierz rearrangement on four spinors (see appendix D).Vector multiplet — A multiplet containing a vector field. In N = 1 supergravity, it contains a real vector, aMajorana spinor and an (auxiliary) scalar D.Scalar multiplet — A multiplet containing scalar fields. In N = 1 supergravity it contains a Majoranaspinor and two propagating and two auxiliary spin 0 fields.Multiplets — Irreducible representations of superalgebras. In global supersymmetry, these representationsare linear, in supergravity they are nonlinear in fields.Supercovariant — An object whose supersymmetry variation does not contain terms with 0,, .L. ConventionsIn order to facilitate comparison between the conventions used in this report and those used by otherauthors, we give here a table of translations