Conformal symmetry superalgebras

Abstract

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 seven. Moreover, in dimensions three, four, five and six, 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.

21 pages, v2: reference added

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• Three-dimensional N=2 supergravity theories: From superspace to components
• de Sitter Supersymmetry Revisited
• Symmetries of curved superspace in five dimensions
• Superconformal quantum field theory in curved spacetime
• The Thermal Bath of de Sitter from Holography
• Twistor spinors and extended conformal superalgebras
• Generalized symmetry superalgebras
• Extended superalgebras from twistor and Killing spinors
• SO(d,1)-invariant Yang-Baxter operators and the dS/CFT correspondence
• Conformal superalgebras via tractor calculus
• Self-consistency of Conformally Coupled ABJM Theory at the Quantum Level
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions
• Rigidity of Killing-Yano and conformal Killing-Yano superalgebras
• Submaximal conformal symmetry superalgebras for Lorentzian manifolds of low dimension