Abstract
We propose supertwistor realisations of (p, q) anti-de Sitter (AdS) superspaces in three dimensions and {mathcal {N}}-extended AdS superspaces in four dimensions. For each superspace, we identify a two-point function that is invariant under the corresponding isometry supergroup. This two-point function is a supersymmetric extension (of a function) of the geodesic distance. We also describe a bi-supertwistor formulation for {mathcal {N}}-extended AdS superspace in four dimensions and harmonic/projective extensions of (p, q) AdS superspaces in three dimensions.
Highlights
In the Appendix we describe a supertwistor realisation of two-dimensional compactified Minkowski superspace M(2|p,q)
SL(2, R) × SO( p) × SO(q) which may be viewed as maximally supersymmetric solutions of ( p, q) anti-de Sitter (AdS) supergravity theories [37]
In this paper we have presented supersymmetric extensions of the twistor descriptions of AdS3 and AdS4
Summary
T = (TA) = Tα , Ti (Tα ) = gfαβ , α, β = 1, 2 i = 1, . 2. the components TA of a pure supertwistor have the following Grassmann parities ε(TA) = ε(T ) + εA (mod 2),. Which allows us to define a graded symplectic inner product on the space of pure supertwistors by the rule: for arbitrary pure supertwistors T and S, the inner product is
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