Superconformal structures on the three-sphere

Abstract

With the motivation to develop superconformal field theory on S^3, we introduce a 2n-extended supersphere S^{3|4n}, with n=1,2,..., as a homogeneous space of the three-dimensional Euclidean superconformal group OSp(2n|2,2) such that its bosonic body is S^3. Supertwistor and bi-supertwistor realizations of S^{3|4n} are derived. We study in detail the n=1 case, which is unique in the sense that the R-symmetry subgroup SO^*(2n) of the superconformal group is compact only for n=1. In particular, we show that the OSp(2|2,2) transformations preserve the chiral subspace of S^{3|4}. Several supercoset realizations of S^{3|4n} are presented. Harmonic/projective extensions of the supersphere by auxiliary bosonic fibre directions are sketched.

44 pages; V2: references added, typos corrected; V3: comments in Appendix B corrected

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• Nilpotent chiral superfield in N=2 supergravity and partial rigid supersymmetry breaking
• Superconformal mechanics in SU(2|1) superspace
• Supersymmetric dS/CFT
• SU(2|1) mechanics and harmonic superspace
• Supertwistor realisations of AdS superspaces
• Embedding formalism for $\mathcal{N}$-extended AdS superspace in four dimensions
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions