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.
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Kuzenko, S.M., Sorokin, D. Superconformal structures on the three-sphere. J. High Energ. Phys. 2014, 80 (2014). https://doi.org/10.1007/JHEP10(2014)080
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DOI: https://doi.org/10.1007/JHEP10(2014)080