Conformal symmetry superalgebras

We show how the rigid conformal supersymmetries associated with a certain class of pseudo-Riemannian spin manifolds define a Lie superalgebra. The even part of this superalgebra contains conformal isometries and constant R-symmetries. The odd part is generated by twistor spinors valued in a particular R-symmetry representation. We prove that any manifold which admits a conformal symmetry superalgebra of this type must generically have dimension less than 7. Moreover, in dimensions 3, 4, 5 and 6, we provide the generic data from which the conformal symmetry superalgebra is prescribed. For conformally flat metrics in these dimensions, and compact R-symmetry, we identify each of the associated conformal symmetry superalgebras with one of the conformal superalgebras classified by Nahm. We also describe several examples for Lorentzian metrics that are not conformally flat.